Степенуване (математика)

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class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Облик"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Облик" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Облик</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_bg.wikipedia.org&uselang=bg" class=""><span>Направете дарение</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B8:%D0%A1%D1%8A%D0%B7%D0%B4%D0%B0%D0%B2%D0%B0%D0%BD%D0%B5_%D0%BD%D0%B0_%D1%81%D0%BC%D0%B5%D1%82%D0%BA%D0%B0&returnto=%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%83%D0%B2%D0%B0%D0%BD%D0%B5+%28%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%29" title="Насърчаваме Ви да си създадете сметка и да влезете, въпреки че не е задължително." class=""><span>Създаване на сметка</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B8:%D0%A0%D0%B5%D0%B3%D0%B8%D1%81%D1%82%D1%80%D0%B8%D1%80%D0%B0%D0%BD%D0%B5_%D0%B8%D0%BB%D0%B8_%D0%B2%D0%BB%D0%B8%D0%B7%D0%B0%D0%BD%D0%B5&returnto=%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%83%D0%B2%D0%B0%D0%BD%D0%B5+%28%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%29" title="Препоръчваме Ви да влезете, въпреки, че не е задължително. [o]" accesskey="o" class=""><span>Влизане</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Допълнителни опции" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Лични инструменти" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Лични инструменти</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Потребителско меню" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_bg.wikipedia.org&uselang=bg"><span>Направете дарение</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B8:%D0%A1%D1%8A%D0%B7%D0%B4%D0%B0%D0%B2%D0%B0%D0%BD%D0%B5_%D0%BD%D0%B0_%D1%81%D0%BC%D0%B5%D1%82%D0%BA%D0%B0&returnto=%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%83%D0%B2%D0%B0%D0%BD%D0%B5+%28%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%29" title="Насърчаваме Ви да си създадете сметка и да влезете, въпреки че не е задължително."><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Създаване на сметка</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B8:%D0%A0%D0%B5%D0%B3%D0%B8%D1%81%D1%82%D1%80%D0%B8%D1%80%D0%B0%D0%BD%D0%B5_%D0%B8%D0%BB%D0%B8_%D0%B2%D0%BB%D0%B8%D0%B7%D0%B0%D0%BD%D0%B5&returnto=%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%83%D0%B2%D0%B0%D0%BD%D0%B5+%28%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%29" title="Препоръчваме Ви да влезете, въпреки, че не е задължително. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Влизане</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Страници за излезли от системата редактори <a href="/wiki/%D0%9F%D0%BE%D0%BC%D0%BE%D1%89:%D0%92%D1%8A%D0%B2%D0%B5%D0%B4%D0%B5%D0%BD%D0%B8%D0%B5" aria-label="Научете повече за редактирането"><span>научете повече</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B8:%D0%9C%D0%BE%D0%B8%D1%82%D0%B5_%D0%BF%D1%80%D0%B8%D0%BD%D0%BE%D1%81%D0%B8" title="Списък на промените, направени от този IP адрес [y]" accesskey="y"><span>Приноси</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B8:%D0%9C%D0%BE%D1%8F%D1%82%D0%B0_%D0%B1%D0%B5%D1%81%D0%B5%D0%B4%D0%B0" title="Дискусия относно редакциите от този адрес [n]" accesskey="n"><span>Беседа</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Сайт"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Съдържание" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Съдържание</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">преместване към страничната лента</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">скриване</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Начало</div> </a> </li> <li id="toc-Математическо_определение" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Математическо_определение"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Математическо определение</span> </div> </a> <ul id="toc-Математическо_определение-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Следствия" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Следствия"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Следствия</span> </div> </a> <button aria-controls="toc-Следствия-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Превключване на подраздел Следствия</span> </button> <ul id="toc-Следствия-sublist" class="vector-toc-list"> <li id="toc-Друго" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Друго"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Друго</span> </div> </a> <ul id="toc-Друго-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Правила" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Правила"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Правила</span> </div> </a> <ul id="toc-Правила-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Отрицателни_степенни_показатели" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Отрицателни_степенни_показатели"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Отрицателни степенни показатели</span> </div> </a> <ul id="toc-Отрицателни_степенни_показатели-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Дробни_(рационални)_степени" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Дробни_(рационални)_степени"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Дробни (рационални) степени</span> </div> </a> <ul id="toc-Дробни_(рационални)_степени-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Вижте_също" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Вижте_също"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Вижте също</span> </div> </a> <ul id="toc-Вижте_също-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Външни_препратки" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Външни_препратки"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Външни препратки</span> </div> </a> <ul id="toc-Външни_препратки-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Съдържание" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Скриване/показване на съдържанието" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Скриване/показване на съдържанието</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Степенуване (математика)</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Към статията на друг език. Налична на 89 езика" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-89" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">89 езика</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Magsverheffing" title="Magsverheffing – африканс" lang="af" hreflang="af" data-title="Magsverheffing" data-language-autonym="Afrikaans" data-language-local-name="африканс" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Potenz_(Mathematik)" title="Potenz (Mathematik) – швейцарски немски" lang="gsw" hreflang="gsw" data-title="Potenz (Mathematik)" data-language-autonym="Alemannisch" data-language-local-name="швейцарски немски" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8A%95%E1%88%B4%E1%89%B5" title="ንሴት – амхарски" lang="am" hreflang="am" data-title="ንሴት" data-language-autonym="አማርኛ" data-language-local-name="амхарски" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B1%D9%81%D8%B9_%D8%A3%D8%B3%D9%8A" title="رفع أسي – арабски" lang="ar" hreflang="ar" data-title="رفع أسي" data-language-autonym="العربية" data-language-local-name="арабски" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Potenciaci%C3%B3n" title="Potenciación – астурски" lang="ast" hreflang="ast" data-title="Potenciación" data-language-autonym="Asturianu" data-language-local-name="астурски" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Q%C3%BCvv%C9%99t%C9%99_y%C3%BCks%C9%99ltm%C9%99" title="Qüvvətə yüksəltmə – азербайджански" lang="az" hreflang="az" data-title="Qüvvətə yüksəltmə" data-language-autonym="Azərbaycanca" data-language-local-name="азербайджански" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%94%D3%99%D1%80%D3%99%D0%B6%D3%99%D0%B3%D3%99_%D0%BA%D2%AF%D1%82%D3%99%D1%80%D0%B5%D2%AF" title="Дәрәжәгә күтәреү – башкирски" lang="ba" hreflang="ba" data-title="Дәрәжәгә күтәреү" data-language-autonym="Башҡортса" data-language-local-name="башкирски" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Eksponentasyon" title="Eksponentasyon – Central Bikol" lang="bcl" hreflang="bcl" data-title="Eksponentasyon" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A1%D1%82%D1%83%D0%BF%D0%B5%D0%BD%D1%8F%D0%B2%D0%B0%D0%BD%D0%BD%D0%B5" title="Ступеняванне – беларуски" lang="be" hreflang="be" data-title="Ступеняванне" data-language-autonym="Беларуская" data-language-local-name="беларуски" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A7%82%E0%A6%9A%E0%A6%95%E0%A7%80%E0%A6%95%E0%A6%B0%E0%A6%A3" title="সূচকীকরণ – бенгалски" lang="bn" hreflang="bn" data-title="সূচকীকরণ" data-language-autonym="বাংলা" data-language-local-name="бенгалски" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Eksponent" title="Eksponent – босненски" lang="bs" hreflang="bs" data-title="Eksponent" data-language-autonym="Bosanski" data-language-local-name="босненски" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-bxr mw-list-item"><a href="https://bxr.wikipedia.org/wiki/%D0%97%D1%8D%D1%80%D0%B3%D1%8D%D0%B4%D1%8D_%D0%B4%D1%8D%D0%B1%D0%B6%D2%AF%D2%AF%D0%BB%D1%85%D1%8D" title="Зэргэдэ дэбжүүлхэ – Russia Buriat" lang="bxr" hreflang="bxr" data-title="Зэргэдэ дэбжүүлхэ" data-language-autonym="Буряад" data-language-local-name="Russia Buriat" class="interlanguage-link-target"><span>Буряад</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Potenciaci%C3%B3" title="Potenciació – каталонски" lang="ca" hreflang="ca" data-title="Potenciació" data-language-autonym="Català" data-language-local-name="каталонски" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AA%D9%88%D8%A7%D9%86_(%D9%85%D8%A7%D8%AA%D9%85%D8%A7%D8%AA%DB%8C%DA%A9)" title="توان (ماتماتیک) – кюрдски (централен)" lang="ckb" hreflang="ckb" data-title="توان (ماتماتیک)" data-language-autonym="کوردی" data-language-local-name="кюрдски (централен)" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Umoc%C5%88ov%C3%A1n%C3%AD" title="Umocňování – чешки" lang="cs" hreflang="cs" data-title="Umocňování" data-language-autonym="Čeština" data-language-local-name="чешки" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9A%D0%B0%D0%BF%D0%B0%D1%88%D1%82%D0%B0%D1%80%D1%83" title="Капаштару – чувашки" lang="cv" hreflang="cv" data-title="Капаштару" data-language-autonym="Чӑвашла" data-language-local-name="чувашки" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Esbonydd" title="Esbonydd – уелски" lang="cy" hreflang="cy" data-title="Esbonydd" data-language-autonym="Cymraeg" data-language-local-name="уелски" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Potens_(matematik)" title="Potens (matematik) – датски" lang="da" hreflang="da" data-title="Potens (matematik)" data-language-autonym="Dansk" data-language-local-name="датски" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Potenz_(Mathematik)" title="Potenz (Mathematik) – немски" lang="de" hreflang="de" data-title="Potenz (Mathematik)" data-language-autonym="Deutsch" data-language-local-name="немски" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%94%CF%8D%CE%BD%CE%B1%CE%BC%CE%B7_(%CE%BC%CE%B1%CE%B8%CE%B7%CE%BC%CE%B1%CF%84%CE%B9%CE%BA%CE%AC)" title="Δύναμη (μαθηματικά) – гръцки" lang="el" hreflang="el" data-title="Δύναμη (μαθηματικά)" data-language-autonym="Ελληνικά" data-language-local-name="гръцки" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Exponentiation" title="Exponentiation – английски" lang="en" hreflang="en" data-title="Exponentiation" data-language-autonym="English" data-language-local-name="английски" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Potenco_(matematiko)" title="Potenco (matematiko) – есперанто" lang="eo" hreflang="eo" data-title="Potenco (matematiko)" data-language-autonym="Esperanto" data-language-local-name="есперанто" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Potenciaci%C3%B3n" title="Potenciación – испански" lang="es" hreflang="es" data-title="Potenciación" data-language-autonym="Español" data-language-local-name="испански" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Astendamine" title="Astendamine – естонски" lang="et" hreflang="et" data-title="Astendamine" data-language-autonym="Eesti" data-language-local-name="естонски" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Berreketa" title="Berreketa – баски" lang="eu" hreflang="eu" data-title="Berreketa" data-language-autonym="Euskara" data-language-local-name="баски" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AA%D9%88%D8%A7%D9%86_(%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C)" title="توان (ریاضی) – персийски" lang="fa" hreflang="fa" data-title="توان (ریاضی)" data-language-autonym="فارسی" data-language-local-name="персийски" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Potenssi" title="Potenssi – фински" lang="fi" hreflang="fi" data-title="Potenssi" data-language-autonym="Suomi" data-language-local-name="фински" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fo mw-list-item"><a href="https://fo.wikipedia.org/wiki/Potensur" title="Potensur – фарьорски" lang="fo" hreflang="fo" data-title="Potensur" data-language-autonym="Føroyskt" data-language-local-name="фарьорски" class="interlanguage-link-target"><span>Føroyskt</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Exponentiation" title="Exponentiation – френски" lang="fr" hreflang="fr" data-title="Exponentiation" data-language-autonym="Français" data-language-local-name="френски" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Potens" title="Potens – северен фризийски" lang="frr" hreflang="frr" data-title="Potens" data-language-autonym="Nordfriisk" data-language-local-name="северен фризийски" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Easp%C3%B3nant" title="Easpónant – ирландски" lang="ga" hreflang="ga" data-title="Easpónant" data-language-autonym="Gaeilge" data-language-local-name="ирландски" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E5%86%AA" title="冪 – Gan" lang="gan" hreflang="gan" data-title="冪" data-language-autonym="贛語" data-language-local-name="Gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Eksponansyasyon" title="Eksponansyasyon – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Eksponansyasyon" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Potenciaci%C3%B3n" title="Potenciación – галисийски" lang="gl" hreflang="gl" data-title="Potenciación" data-language-autonym="Galego" data-language-local-name="галисийски" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he badge-Q17437796 badge-featuredarticle mw-list-item" title="Избрана статия"><a href="https://he.wikipedia.org/wiki/%D7%97%D7%96%D7%A7%D7%94_(%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94)" title="חזקה (מתמטיקה) – иврит" lang="he" hreflang="he" data-title="חזקה (מתמטיקה)" data-language-autonym="עברית" data-language-local-name="иврит" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%98%E0%A4%BE%E0%A4%A4%E0%A4%BE%E0%A4%82%E0%A4%95" title="घातांक – хинди" lang="hi" hreflang="hi" data-title="घातांक" data-language-autonym="हिन्दी" data-language-local-name="хинди" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Potenciranje" title="Potenciranje – хърватски" lang="hr" hreflang="hr" data-title="Potenciranje" data-language-autonym="Hrvatski" data-language-local-name="хърватски" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Hatv%C3%A1ny" title="Hatvány – унгарски" lang="hu" hreflang="hu" data-title="Hatvány" data-language-autonym="Magyar" data-language-local-name="унгарски" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B1%D5%BD%D5%BF%D5%AB%D5%B3%D5%A1%D5%B6_(%D5%B0%D5%A1%D5%B6%D6%80%D5%A1%D5%B0%D5%A1%D5%B7%D5%AB%D5%BE)" title="Աստիճան (հանրահաշիվ) – арменски" lang="hy" hreflang="hy" data-title="Աստիճան (հանրահաշիվ)" data-language-autonym="Հայերեն" data-language-local-name="арменски" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Potentiation" title="Potentiation – интерлингва" lang="ia" hreflang="ia" data-title="Potentiation" data-language-autonym="Interlingua" data-language-local-name="интерлингва" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Eksponensiasi" title="Eksponensiasi – индонезийски" lang="id" hreflang="id" data-title="Eksponensiasi" data-language-autonym="Bahasa Indonesia" data-language-local-name="индонезийски" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Potenco" title="Potenco – идо" lang="io" hreflang="io" data-title="Potenco" data-language-autonym="Ido" data-language-local-name="идо" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Veldi_(st%C3%A6r%C3%B0fr%C3%A6%C3%B0i)" title="Veldi (stærðfræði) – исландски" lang="is" hreflang="is" data-title="Veldi (stærðfræði)" data-language-autonym="Íslenska" data-language-local-name="исландски" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Potenza_(matematica)" title="Potenza (matematica) – италиански" lang="it" hreflang="it" data-title="Potenza (matematica)" data-language-autonym="Italiano" data-language-local-name="италиански" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%86%AA%E4%B9%97" title="冪乗 – японски" lang="ja" hreflang="ja" data-title="冪乗" data-language-autonym="日本語" data-language-local-name="японски" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Exponenshieshan" title="Exponenshieshan – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Exponenshieshan" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%94%D3%99%D1%80%D0%B5%D0%B6%D0%B5%D0%BB%D0%B5%D1%83" title="Дәрежелеу – казахски" lang="kk" hreflang="kk" data-title="Дәрежелеу" data-language-autonym="Қазақша" data-language-local-name="казахски" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B1%B0%EB%93%AD%EC%A0%9C%EA%B3%B1" title="거듭제곱 – корейски" lang="ko" hreflang="ko" data-title="거듭제곱" data-language-autonym="한국어" data-language-local-name="корейски" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Potentia_(mathematica)" title="Potentia (mathematica) – латински" lang="la" hreflang="la" data-title="Potentia (mathematica)" data-language-autonym="Latina" data-language-local-name="латински" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Esponenti" title="Esponenti – Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Esponenti" data-language-autonym="Lingua Franca Nova" data-language-local-name="Lingua Franca Nova" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Machsverh%C3%B6ffing" title="Machsverhöffing – лимбургски" lang="li" hreflang="li" data-title="Machsverhöffing" data-language-autonym="Limburgs" data-language-local-name="лимбургски" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/K%C4%97limas_laipsniu" title="Kėlimas laipsniu – литовски" lang="lt" hreflang="lt" data-title="Kėlimas laipsniu" data-language-autonym="Lietuvių" data-language-local-name="литовски" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/K%C4%81pin%C4%81%C5%A1ana" title="Kāpināšana – латвийски" lang="lv" hreflang="lv" data-title="Kāpināšana" data-language-autonym="Latviešu" data-language-local-name="латвийски" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Toraka_(matematika)" title="Toraka (matematika) – малгашки" lang="mg" hreflang="mg" data-title="Toraka (matematika)" data-language-autonym="Malagasy" data-language-local-name="малгашки" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%83%D0%B2%D0%B0%D1%9A%D0%B5" title="Степенување – македонски" lang="mk" hreflang="mk" data-title="Степенување" data-language-autonym="Македонски" data-language-local-name="македонски" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Pengeksponenan" title="Pengeksponenan – малайски" lang="ms" hreflang="ms" data-title="Pengeksponenan" data-language-autonym="Bahasa Melayu" data-language-local-name="малайски" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%98%E0%A4%BE%E0%A4%A4%E0%A4%BE%E0%A4%99%E0%A5%8D%E0%A4%95" title="घाताङ्क – непалски" lang="ne" hreflang="ne" data-title="घाताङ्क" data-language-autonym="नेपाली" data-language-local-name="непалски" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Machtsverheffen" title="Machtsverheffen – нидерландски" lang="nl" hreflang="nl" data-title="Machtsverheffen" data-language-autonym="Nederlands" data-language-local-name="нидерландски" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Potens_i_matematikk" title="Potens i matematikk – норвежки (нюношк)" lang="nn" hreflang="nn" data-title="Potens i matematikk" data-language-autonym="Norsk nynorsk" data-language-local-name="норвежки (нюношк)" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Potens_(matematikk)" title="Potens (matematikk) – норвежки (букмол)" lang="nb" hreflang="nb" data-title="Potens (matematikk)" data-language-autonym="Norsk bokmål" data-language-local-name="норвежки (букмол)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Aangessoo(ekispoonentii)" title="Aangessoo(ekispoonentii) – оромо" lang="om" hreflang="om" data-title="Aangessoo(ekispoonentii)" data-language-autonym="Oromoo" data-language-local-name="оромо" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%98%E0%A8%BE%E0%A8%A4_%E0%A8%85%E0%A9%B0%E0%A8%95" title="ਘਾਤ ਅੰਕ – пенджабски" lang="pa" hreflang="pa" data-title="ਘਾਤ ਅੰਕ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="пенджабски" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Pot%C4%99gowanie" title="Potęgowanie – полски" lang="pl" hreflang="pl" data-title="Potęgowanie" data-language-autonym="Polski" data-language-local-name="полски" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Exponencia%C3%A7%C3%A3o" title="Exponenciação – португалски" lang="pt" hreflang="pt" data-title="Exponenciação" data-language-autonym="Português" data-language-local-name="португалски" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Yupa_huqariy" title="Yupa huqariy – кечуа" lang="qu" hreflang="qu" data-title="Yupa huqariy" data-language-autonym="Runa Simi" data-language-local-name="кечуа" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Putere_(matematic%C4%83)" title="Putere (matematică) – румънски" lang="ro" hreflang="ro" data-title="Putere (matematică)" data-language-autonym="Română" data-language-local-name="румънски" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%92%D0%BE%D0%B7%D0%B2%D0%B5%D0%B4%D0%B5%D0%BD%D0%B8%D0%B5_%D0%B2_%D1%81%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%8C" title="Возведение в степень – руски" lang="ru" hreflang="ru" data-title="Возведение в степень" data-language-autonym="Русский" data-language-local-name="руски" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%91%D2%AF%D1%82%D2%AF%D0%BD_%D0%BA%D3%A9%D1%80%D0%B4%D3%A9%D1%80%D3%A9%D3%A9%D1%87%D1%87%D2%AF%D0%BB%D1%8D%D1%8D%D1%85_%D1%81%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%8C" title="Бүтүн көрдөрөөччүлээх степень – саха" lang="sah" hreflang="sah" data-title="Бүтүн көрдөрөөччүлээх степень" data-language-autonym="Саха тыла" data-language-local-name="саха" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Putenza_(matim%C3%A0tica)" title="Putenza (matimàtica) – сицилиански" lang="scn" hreflang="scn" data-title="Putenza (matimàtica)" data-language-autonym="Sicilianu" data-language-local-name="сицилиански" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Stepenovanje" title="Stepenovanje – сърбохърватски" lang="sh" hreflang="sh" data-title="Stepenovanje" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="сърбохърватски" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Exponentiation" title="Exponentiation – Simple English" lang="en-simple" hreflang="en-simple" data-title="Exponentiation" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Umoc%C5%88ovanie" title="Umocňovanie – словашки" lang="sk" hreflang="sk" data-title="Umocňovanie" data-language-autonym="Slovenčina" data-language-local-name="словашки" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Potenciranje" title="Potenciranje – словенски" lang="sl" hreflang="sl" data-title="Potenciranje" data-language-autonym="Slovenščina" data-language-local-name="словенски" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Kutambanura_(nhamba)" title="Kutambanura (nhamba) – шона" lang="sn" hreflang="sn" data-title="Kutambanura (nhamba)" data-language-autonym="ChiShona" data-language-local-name="шона" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D0%BE%D0%B2%D0%B0%D1%9A%D0%B5" title="Степеновање – сръбски" lang="sr" hreflang="sr" data-title="Степеновање" data-language-autonym="Српски / srpski" data-language-local-name="сръбски" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Potens" title="Potens – шведски" lang="sv" hreflang="sv" data-title="Potens" data-language-autonym="Svenska" data-language-local-name="шведски" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%85%E0%AE%9F%E0%AF%81%E0%AE%95%E0%AF%8D%E0%AE%95%E0%AF%87%E0%AE%B1%E0%AF%8D%E0%AE%B1%E0%AE%AE%E0%AF%8D" title="அடுக்கேற்றம் – тамилски" lang="ta" hreflang="ta" data-title="அடுக்கேற்றம்" data-language-autonym="தமிழ்" data-language-local-name="тамилски" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th badge-Q17437798 badge-goodarticle mw-list-item" title="Добра статия"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%A2%E0%B8%81%E0%B8%81%E0%B8%B3%E0%B8%A5%E0%B8%B1%E0%B8%87" title="การยกกำลัง – тайски" lang="th" hreflang="th" data-title="การยกกำลัง" data-language-autonym="ไทย" data-language-local-name="тайски" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Pagpapalakas_(matematika)" title="Pagpapalakas (matematika) – тагалог" lang="tl" hreflang="tl" data-title="Pagpapalakas (matematika)" data-language-autonym="Tagalog" data-language-local-name="тагалог" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%C3%9Cs" title="Üs – турски" lang="tr" hreflang="tr" data-title="Üs" data-language-autonym="Türkçe" data-language-local-name="турски" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-ug mw-list-item"><a href="https://ug.wikipedia.org/wiki/%D8%AF%DB%95%D8%B1%D9%89%D8%AC%DB%95_(%D9%85%D8%A7%D8%AA%DB%90%D9%85%D8%A7%D8%AA%D9%89%D9%83%D8%A7)" title="دەرىجە (ماتېماتىكا) – уйгурски" lang="ug" hreflang="ug" data-title="دەرىجە (ماتېماتىكا)" data-language-autonym="ئۇيغۇرچە / Uyghurche" data-language-local-name="уйгурски" class="interlanguage-link-target"><span>ئۇيغۇرچە / Uyghurche</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9F%D1%96%D0%B4%D0%BD%D0%B5%D1%81%D0%B5%D0%BD%D0%BD%D1%8F_%D0%B4%D0%BE_%D1%81%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%8F" title="Піднесення до степеня – украински" lang="uk" hreflang="uk" data-title="Піднесення до степеня" data-language-autonym="Українська" data-language-local-name="украински" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/L%C5%A9y_th%E1%BB%ABa" title="Lũy thừa – виетнамски" lang="vi" hreflang="vi" data-title="Lũy thừa" data-language-autonym="Tiếng Việt" data-language-local-name="виетнамски" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Eksponentasyon" title="Eksponentasyon – варай" lang="war" hreflang="war" data-title="Eksponentasyon" data-language-autonym="Winaray" data-language-local-name="варай" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%B9%82" title="幂 – ву китайски" lang="wuu" hreflang="wuu" data-title="幂" data-language-autonym="吴语" data-language-local-name="ву китайски" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-xal mw-list-item"><a href="https://xal.wikipedia.org/wiki/%D0%98%D0%B4%D1%80%D0%B8%D0%BB%D2%BB%D0%B0%D0%BD" title="Идрилһан – калмик" lang="xal" hreflang="xal" data-title="Идрилһан" data-language-autonym="Хальмг" data-language-local-name="калмик" class="interlanguage-link-target"><span>Хальмг</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A4%D7%90%D7%98%D7%A2%D7%A0%D7%A5" title="פאטענץ – идиш" lang="yi" hreflang="yi" data-title="פאטענץ" data-language-autonym="ייִדיש" data-language-local-name="идиш" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%86%AA" title="冪 – китайски" lang="zh" hreflang="zh" data-title="冪" data-language-autonym="中文" data-language-local-name="китайски" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%AC%A1%E6%96%B9" title="次方 – кантонски" lang="yue" hreflang="yue" data-title="次方" data-language-autonym="粵語" data-language-local-name="кантонски" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q33456#sitelinks-wikipedia" title="Редактиране на междуезиковите препратки" class="wbc-editpage">Редактиране</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Именни пространства"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%83%D0%B2%D0%B0%D0%BD%D0%B5_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Преглед на основната страница [c]" accesskey="c"><span>Статия</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%D0%91%D0%B5%D1%81%D0%B5%D0%B4%D0%B0:%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%83%D0%B2%D0%B0%D0%BD%D0%B5_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)&action=edit&redlink=1" rel="discussion" class="new" title="Беседа за страницата (страницата не съществува) [t]" accesskey="t"><span>Беседа</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Промяна на езиковия вариант" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">български</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Прегледи"> <div 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[e]" accesskey="e"><span>Редактиране на кода</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%83%D0%B2%D0%B0%D0%BD%D0%B5_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)&action=history" title="Предишни версии на страницата [h]" accesskey="h"><span>История</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Инструменти" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Инструменти</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Инструменти</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">преместване към страничната лента</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">скриване</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Допълнителни опции" > <div class="vector-menu-heading"> Действия </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%83%D0%B2%D0%B0%D0%BD%D0%B5_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)"><span>Преглед</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%83%D0%B2%D0%B0%D0%BD%D0%B5_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)&veaction=edit" title="Редактиране на страницата [v]" accesskey="v"><span>Редактиране</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%83%D0%B2%D0%B0%D0%BD%D0%B5_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)&action=edit" title="Редактиране на изходния код на страницата [e]" accesskey="e"><span>Редактиране на кода</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%83%D0%B2%D0%B0%D0%BD%D0%B5_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)&action=history"><span>История</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Основни </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B8:%D0%9A%D0%B0%D0%BA%D0%B2%D0%BE_%D1%81%D0%BE%D1%87%D0%B8_%D0%BD%D0%B0%D1%81%D0%B0%D0%BC/%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%83%D0%B2%D0%B0%D0%BD%D0%B5_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Списък на всички страници, сочещи насам [j]" accesskey="j"><span>Какво сочи насам</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B8:%D0%A1%D0%B2%D1%8A%D1%80%D0%B7%D0%B0%D0%BD%D0%B8_%D0%BF%D1%80%D0%BE%D0%BC%D0%B5%D0%BD%D0%B8/%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%83%D0%B2%D0%B0%D0%BD%D0%B5_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" rel="nofollow" title="Последните промени на страници, сочени от тази страница [k]" accesskey="k"><span>Свързани промени</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/MediaWiki:Uploadtext" title="Качи файлове [u]" accesskey="u"><span>Качване на 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href="/w/index.php?title=%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B8:QrCode&url=https%3A%2F%2Fbg.wikipedia.org%2Fwiki%2F%25D0%25A1%25D1%2582%25D0%25B5%25D0%25BF%25D0%25B5%25D0%25BD%25D1%2583%25D0%25B2%25D0%25B0%25D0%25BD%25D0%25B5_%28%25D0%25BC%25D0%25B0%25D1%2582%25D0%25B5%25D0%25BC%25D0%25B0%25D1%2582%25D0%25B8%25D0%25BA%25D0%25B0%29"><span>Изтегляне на QR код</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Отпечатване/изнасяне </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B8:Book&bookcmd=book_creator&referer=%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%83%D0%B2%D0%B0%D0%BD%D0%B5+%28%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%29"><span>Създаване на книга</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%B8:DownloadAsPdf&page=%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%83%D0%B2%D0%B0%D0%BD%D0%B5_%28%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%29&action=show-download-screen"><span>Изтегляне като PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%83%D0%B2%D0%B0%D0%BD%D0%B5_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)&printable=yes" title="Версия за печат на страницата [p]" accesskey="p"><span>Версия за печат</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> В други проекти </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Exponentiation" hreflang="en"><span>Общомедия</span></a></li><li class="wb-otherproject-link wb-otherproject-wikifunctions mw-list-item"><a href="https://www.wikifunctions.org/wiki/Z12665" hreflang="en"><span>Wikifunctions</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q33456" title="Препратка към свързания обект от хранилището за данни [g]" accesskey="g"><span>Обект в Уикиданни</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Облик"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Облик</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">преместване към страничната лента</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">скриване</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">от Уикипедия, свободната енциклопедия</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="bg" dir="ltr"><p><b>Степенуването</b> е съкратен запис на произведение на еднакви множители. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Математическо_определение"><span id=".D0.9C.D0.B0.D1.82.D0.B5.D0.BC.D0.B0.D1.82.D0.B8.D1.87.D0.B5.D1.81.D0.BA.D0.BE_.D0.BE.D0.BF.D1.80.D0.B5.D0.B4.D0.B5.D0.BB.D0.B5.D0.BD.D0.B8.D0.B5"></span>Математическо определение</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%83%D0%B2%D0%B0%D0%BD%D0%B5_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)&veaction=edit&section=1" title="Редактиране на раздел: Математическо определение" class="mw-editsection-visualeditor"><span>редактиране</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%83%D0%B2%D0%B0%D0%BD%D0%B5_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)&action=edit&section=1" title="Edit section's source code: Математическо определение"><span>редактиране на кода</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/%D0%A3%D0%BC%D0%BD%D0%BE%D0%B6%D0%B5%D0%BD%D0%B8%D0%B5#Наименования" title="Умножение">Произведението</a> от <i><b>n</b></i> на брой равни <a href="/wiki/%D0%9C%D0%BD%D0%BE%D0%B6%D0%B8%D1%82%D0%B5%D0%BB" class="mw-redirect" title="Множител">множители</a> <i><b>a</b></i>, където <i><b>n</b></i> е <a href="/wiki/%D0%95%D1%81%D1%82%D0%B5%D1%81%D1%82%D0%B2%D0%B5%D0%BD%D0%BE_%D1%87%D0%B8%D1%81%D0%BB%D0%BE" title="Естествено число">естествено число</a>, се записва като <b>a<sup>n</sup></b> и се нарича степенуване на основа <i><b>a</b></i> на степен <i><b>n</b></i>. Целият този процес се нарича <i><b>повдигане на степен</b></i> или <i><b>стeпенуване</b></i>. Изразът <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;5^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <msup> <mn>5</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;5^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dfd035c2b917f481ab8b7f3109f0f3d1258a8594" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.862ex; height:2.676ex;" alt="{\displaystyle \;5^{3}}"></span> се чете <i><b>пет на трета (степен) или пет на степен три</b></i>. Първите две степени, <i>на втора</i> и <i>на трета</i>, се наричат съответно още <i><b>на квадрат</b></i> и <i><b>на куб</b></i>. Така<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;5^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <msup> <mn>5</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;5^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe8fa38c0dd9dbd2799f7d767371db09eb8fa550" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.862ex; height:2.676ex;" alt="{\displaystyle \;5^{2}}"></span> може да се прочете като <i><b>пет на квадрат</b></i>. Числата, получени при повдигането на квадрат на <a href="/wiki/%D0%A6%D1%8F%D0%BB%D0%BE_%D1%87%D0%B8%D1%81%D0%BB%D0%BE" title="Цяло число">цяло число</a>, се наричат <a href="/wiki/%D0%9A%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%BD%D0%BE_%D1%87%D0%B8%D1%81%D0%BB%D0%BE" title="Квадратно число">точни квадрати</a>. </p><p>Когато се работи с числа, обикновено се опростява: например <b>27</b> вместо<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;3^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <msup> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;3^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/848a8eff93687392b5d8b377dd749aefaadaef88" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.862ex; height:2.676ex;" alt="{\displaystyle \;3^{3}}"></span>, но когато се работи с променливи, се използва<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;x^{6}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;x^{6}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f0ad00fae27dbc2210d7cca5f2cc75640e1c9562" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.029ex; height:2.676ex;" alt="{\displaystyle \;x^{6}}"></span> вместо <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;xxxxxx}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <mi>x</mi> <mi>x</mi> <mi>x</mi> <mi>x</mi> <mi>x</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;xxxxxx}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/551aa3d701c9217be23ad4404b422c231ff87308" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.623ex; height:1.676ex;" alt="{\displaystyle \;xxxxxx}"></span>. </p> <div class="mw-heading mw-heading2"><h2 id="Следствия"><span id=".D0.A1.D0.BB.D0.B5.D0.B4.D1.81.D1.82.D0.B2.D0.B8.D1.8F"></span>Следствия</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%83%D0%B2%D0%B0%D0%BD%D0%B5_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)&veaction=edit&section=2" title="Редактиране на раздел: Следствия" class="mw-editsection-visualeditor"><span>редактиране</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%83%D0%B2%D0%B0%D0%BD%D0%B5_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)&action=edit&section=2" title="Edit section's source code: Следствия"><span>редактиране на кода</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Число, повдигнато на степен <b>1</b>, си остава същото (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;a^{1}=a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msup> <mo>=</mo> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;a^{1}=a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e792478435ac33c6108a47aae02ea336dff98b25" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.257ex; height:2.676ex;" alt="{\displaystyle \;a^{1}=a}"></span>).</li> <li>Число, повдигнато на степен <b>0</b> е равно на 1 (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;a^{0}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msup> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;a^{0}=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33d629eb51a0bb81dd536bed3c813fbebd28b6ce" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.19ex; height:2.676ex;" alt="{\displaystyle \;a^{0}=1}"></span>).</li> <li>Число, повдигнато на степен <b>-1</b> е равно на <a href="/wiki/%D0%A0%D0%B5%D1%86%D0%B8%D0%BF%D1%80%D0%BE%D1%87%D0%BD%D0%B0_%D1%81%D1%82%D0%BE%D0%B9%D0%BD%D0%BE%D1%81%D1%82" title="Реципрочна стойност">реципрочното</a> му (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;a^{-1}={1 \over a}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>a</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;a^{-1}={1 \over a}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b1f02894f36f85d0e74ab78bd8401491eb1ee211" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.372ex; height:5.176ex;" alt="{\displaystyle \;a^{-1}={1 \over a}}"></span> при <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;a\neq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <mi>a</mi> <mo>≠</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;a\neq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1592b7f4fecd4f3dc42eb86e0320926c73e680a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.136ex; height:2.676ex;" alt="{\displaystyle \;a\neq 0}"></span>).</li> <li>Число, повдигнато на степен <b>1/2</b> е равно на неговия <a href="/wiki/%D0%9A%D0%BE%D1%80%D0%B5%D0%BD_%D0%BA%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%B5%D0%BD" class="mw-redirect" title="Корен квадратен">корен квадратен</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;a^{\frac {1}{2}}={\sqrt {a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>a</mi> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;a^{\frac {1}{2}}={\sqrt {a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b3a813c1a77bb5ce308c4c7ff894f68d53b5b64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:9.875ex; height:4.176ex;" alt="{\displaystyle \;a^{\frac {1}{2}}={\sqrt {a}}}"></span>).</li> <li>При повдигане на число, различно от 0, на произволна степен резултатът винаги е различен от <b>0</b>.</li> <li>При повдигане на число на <a href="/wiki/%D0%A7%D0%B5%D1%82%D0%BD%D0%BE%D1%81%D1%82" title="Четност">четна</a> степен, резултатът винаги е <a href="/wiki/%D0%9F%D0%BE%D0%BB%D0%BE%D0%B6%D0%B8%D1%82%D0%B5%D0%BB%D0%BD%D0%BE_%D1%87%D0%B8%D1%81%D0%BB%D0%BE" title="Положително число">положително число</a>.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Друго"><span id=".D0.94.D1.80.D1.83.D0.B3.D0.BE"></span>Друго</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%83%D0%B2%D0%B0%D0%BD%D0%B5_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)&veaction=edit&section=3" title="Редактиране на раздел: Друго" class="mw-editsection-visualeditor"><span>редактиране</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%83%D0%B2%D0%B0%D0%BD%D0%B5_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)&action=edit&section=3" title="Edit section's source code: Друго"><span>редактиране на кода</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Сборът на всички степени на числото 2 плюс 1 е равен на следващата степен на 2: 1 + 2<sup>0</sup> + 2<sup>1</sup>...+2<sup>n</sup> = 2<sup>n+1</sup> (за всяко <a href="/wiki/%D0%A6%D1%8F%D0%BB%D0%BE_%D1%87%D0%B8%D1%81%D0%BB%D0%BE" title="Цяло число">цяло число</a> <i>n</i>≥0).</li></ul> <div class="mw-heading mw-heading2"><h2 id="Правила"><span id=".D0.9F.D1.80.D0.B0.D0.B2.D0.B8.D0.BB.D0.B0"></span>Правила</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%83%D0%B2%D0%B0%D0%BD%D0%B5_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)&veaction=edit&section=4" title="Редактиране на раздел: Правила" class="mw-editsection-visualeditor"><span>редактиране</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%83%D0%B2%D0%B0%D0%BD%D0%B5_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)&action=edit&section=4" title="Edit section's source code: Правила"><span>редактиране на кода</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>При степенуването може да се използват следните правила, за да се опростят математически изрази включващи степенуване. </p><p>За да се опрости израза, трябва да заменим с това, което той означава. <i>На трета</i> означава да <i>умножим три пъти</i>, <i>на четвърта</i> – <i>да умножим четири пъти</i>. Използвайки това може да се разшири израза и след това да се опрости. </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;(x^{3})(x^{4})=(xxx)(xxxx)=xxxxxxx=x^{7}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mi>x</mi> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mi>x</mi> <mi>x</mi> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>x</mi> <mi>x</mi> <mi>x</mi> <mi>x</mi> <mi>x</mi> <mi>x</mi> <mi>x</mi> <mo>=</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;(x^{3})(x^{4})=(xxx)(xxxx)=xxxxxxx=x^{7}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e3fccf9678d260ab1b2cee11120c295b99ac5bb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:42.945ex; height:3.176ex;" alt="{\displaystyle \;(x^{3})(x^{4})=(xxx)(xxxx)=xxxxxxx=x^{7}}"></span></dd></dl></dd></dl> <p>Следователно <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;x^{7}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;x^{7}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77702c4aeebd604d2e07c459539d5fa453bb4d84" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.029ex; height:2.676ex;" alt="{\displaystyle \;x^{7}}"></span> е равно на <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;x^{(3+4)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>3</mn> <mo>+</mo> <mn>4</mn> <mo stretchy="false">)</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;x^{(3+4)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e998736f6c63c61a17353160b6deaf2a00c33164" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.409ex; height:2.843ex;" alt="{\displaystyle \;x^{(3+4)}}"></span>. </p> <ul><li><b>Първото правило при степенуването</b>:</li></ul> <p>Умножение на степенни изрази с <b>еднаква база</b> може да се представи като <i>база</i> със <b>степенен показател равен на сумата от степенните показатели</b>, както в израза: </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;(x^{m})(x^{n})=x^{(m+n)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>m</mi> <mo>+</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;(x^{m})(x^{n})=x^{(m+n)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/67096b5cef626463a75368a14da91726b5fbdfa6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.464ex; height:3.343ex;" alt="{\displaystyle \;(x^{m})(x^{n})=x^{(m+n)}}"></span></dd></dl></dd></dl> <p><b>Нe</b> може да се прилага това правило при изрази с различни <i>бази</i>. Например изразът <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;(x^{4})(y^{3})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;(x^{4})(y^{3})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f69aafff87b127d68f163e13c9c7d4f4f07fd66b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.862ex; height:3.176ex;" alt="{\displaystyle \;(x^{4})(y^{3})}"></span> не може да се опрости, защото <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;(x^{4})(y^{3})=xxxxyyy=(x^{4})(y^{3})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo>=</mo> <mi>x</mi> <mi>x</mi> <mi>x</mi> <mi>x</mi> <mi>y</mi> <mi>y</mi> <mi>y</mi> <mo>=</mo> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;(x^{4})(y^{3})=xxxxyyy=(x^{4})(y^{3})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/44b7c8e05ea68d44813f39eb928089b4c2b23b3f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:32.062ex; height:3.176ex;" alt="{\displaystyle \;(x^{4})(y^{3})=xxxxyyy=(x^{4})(y^{3})}"></span> – и не е възможно комбинирането. </p> <ul><li><b>Второто правилото при степенуването</b>:</li></ul> <p>Използвайки същата логика може да се замести израза <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;{(x^{2})}^{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;{(x^{2})}^{4}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0486c978118d196b39ff98190b1241ed3a6513f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.893ex; height:3.676ex;" alt="{\displaystyle \;{(x^{2})}^{4}}"></span> с неговото значение - „на четвърта“ означава да се умножи четири пъти <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \quad x^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="1em" /> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \quad x^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30b415d62fc1d2a4e6c54fb08124c8da602f9019" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.707ex; height:2.676ex;" alt="{\displaystyle \quad x^{2}}"></span>. </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;{(x^{2})}^{4}=(x^{2})(x^{2})(x^{2})(x^{2})=(xx)(xx)(xx)(xx)=xxxxxxxx=x^{8}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>x</mi> <mi>x</mi> <mi>x</mi> <mi>x</mi> <mi>x</mi> <mi>x</mi> <mi>x</mi> <mi>x</mi> <mo>=</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;{(x^{2})}^{4}=(x^{2})(x^{2})(x^{2})(x^{2})=(xx)(xx)(xx)(xx)=xxxxxxxx=x^{8}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/19768bb86363cedf17296348e0d1f57bc7fe766c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:65.955ex; height:3.676ex;" alt="{\displaystyle \;{(x^{2})}^{4}=(x^{2})(x^{2})(x^{2})(x^{2})=(xx)(xx)(xx)(xx)=xxxxxxxx=x^{8}}"></span>.<br /></dd></dl></dd></dl> <p>Отново резултатът <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;x^{8}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;x^{8}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/55e9e65882c3e8f3c67fc67eb2127cbea7777008" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.029ex; height:2.676ex;" alt="{\displaystyle \;x^{8}}"></span> е равен на <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;x^{(2\times 4)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>2</mn> <mo>×</mo> <mn>4</mn> <mo stretchy="false">)</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;x^{(2\times 4)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e2829949177c6799c9417ba9b7b6abaeafe6dac2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.409ex; height:2.843ex;" alt="{\displaystyle \;x^{(2\times 4)}}"></span> </p><p>В това се заключава правилото, че <b>степенен израз повдигнат на степен</b> може да се замени с израз, при който <b>базата е повдигната на степен равна на произведението от стeпeнните показатели</b> както в израза. </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;{(x^{m})}^{n}=x^{(m\times n)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>=</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>m</mi> <mo>×</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;{(x^{m})}^{n}=x^{(m\times n)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a7a8fd5e40d5ad9b744bd34c177f8bca185e6601" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.325ex; height:3.343ex;" alt="{\displaystyle \;{(x^{m})}^{n}=x^{(m\times n)}}"></span>.</dd></dl></dd></dl> <ul><li><b>Трето правило при степенуването:</b></li></ul> <p>При степенуване на произведение в скоби (хy)<sup>3</sup>, то <b>степента се прилага върху всеки множител от скобите</b>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;{(xy^{2})}^{3}=(xy^{2})(xy^{2})(xy^{2})=(xxx)(y^{2}y^{2}y^{2})=x^{3}y^{6}=(x)^{3}{(y^{2})}^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>x</mi> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <mi>x</mi> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>x</mi> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>x</mi> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mi>x</mi> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;{(xy^{2})}^{3}=(xy^{2})(xy^{2})(xy^{2})=(xxx)(y^{2}y^{2}y^{2})=x^{3}y^{6}=(x)^{3}{(y^{2})}^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0bfab5726ab3847fc6bb64b979896c90d7016199" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:63.63ex; height:3.676ex;" alt="{\displaystyle \;{(xy^{2})}^{3}=(xy^{2})(xy^{2})(xy^{2})=(xxx)(y^{2}y^{2}y^{2})=x^{3}y^{6}=(x)^{3}{(y^{2})}^{3}}"></span>.</dd></dl> <p>И още един пример: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;\left({\frac {x}{y}}\right)^{2}={\frac {x^{2}}{y^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mi>y</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;\left({\frac {x}{y}}\right)^{2}={\frac {x^{2}}{y^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c4eb7b99718e6336e32b8a28f019c11962d9a90c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:13.605ex; height:6.509ex;" alt="{\displaystyle \;\left({\frac {x}{y}}\right)^{2}={\frac {x^{2}}{y^{2}}}}"></span>.</dd></dl> <p>Погрешно ще бъде прилагането на това правило, ако в скобите е записана сума или разлика, например: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \quad (3+4)^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="1em" /> <mo stretchy="false">(</mo> <mn>3</mn> <mo>+</mo> <mn>4</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \quad (3+4)^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bfe91b42882dd2e7da0d8443e44a7b9835f7a3ea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.351ex; height:3.176ex;" alt="{\displaystyle \quad (3+4)^{2}}"></span> <b><big>не</big></b> може да стане<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \quad 3^{2}+4^{2}=9+16=25}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="1em" /> <msup> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mn>4</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>9</mn> <mo>+</mo> <mn>16</mn> <mo>=</mo> <mn>25</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \quad 3^{2}+4^{2}=9+16=25}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d4b59b3b782b22ba7acfa0fd33f84beb256d24ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:24.446ex; height:2.843ex;" alt="{\displaystyle \quad 3^{2}+4^{2}=9+16=25}"></span>, защото резултатът е грешен. Правилното изчисление е <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \quad (3+4)^{2}=(7)^{2}=49}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="1em" /> <mo stretchy="false">(</mo> <mn>3</mn> <mo>+</mo> <mn>4</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <mn>7</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>49</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \quad (3+4)^{2}=(7)^{2}=49}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f4ee813dab1392310f36c10363b1986cd99e5b60" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.899ex; height:3.176ex;" alt="{\displaystyle \quad (3+4)^{2}=(7)^{2}=49}"></span>.</dd></dl> <p>По-добре е да се запише според това, че „на квадрат“ означава сумата или разликата да се умножи веднъж сама по себе си, така че <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;{(x-2)}^{2}=(x-2)(x-2)=xx-2x-2x+4=x^{2}-4x+4}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mi>x</mi> <mi>x</mi> <mo>−</mo> <mn>2</mn> <mi>x</mi> <mo>−</mo> <mn>2</mn> <mi>x</mi> <mo>+</mo> <mn>4</mn> <mo>=</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>4</mn> <mi>x</mi> <mo>+</mo> <mn>4</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;{(x-2)}^{2}=(x-2)(x-2)=xx-2x-2x+4=x^{2}-4x+4}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4da964ddec33ab107ffd836adb2f377afe9aca25" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:61.467ex; height:3.343ex;" alt="{\displaystyle \;{(x-2)}^{2}=(x-2)(x-2)=xx-2x-2x+4=x^{2}-4x+4}"></span>. Това е част от т.нар. <a href="/wiki/%D0%A4%D0%BE%D1%80%D0%BC%D1%83%D0%BB%D0%B8_%D0%B7%D0%B0_%D1%81%D1%8A%D0%BA%D1%80%D0%B0%D1%82%D0%B5%D0%BD%D0%BE_%D1%83%D0%BC%D0%BD%D0%BE%D0%B6%D0%B5%D0%BD%D0%B8%D0%B5" title="Формули за съкратено умножение">формули за съкратено умножение</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Отрицателни_степенни_показатели"><span id=".D0.9E.D1.82.D1.80.D0.B8.D1.86.D0.B0.D1.82.D0.B5.D0.BB.D0.BD.D0.B8_.D1.81.D1.82.D0.B5.D0.BF.D0.B5.D0.BD.D0.BD.D0.B8_.D0.BF.D0.BE.D0.BA.D0.B0.D0.B7.D0.B0.D1.82.D0.B5.D0.BB.D0.B8"></span>Отрицателни степенни показатели</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%83%D0%B2%D0%B0%D0%BD%D0%B5_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)&veaction=edit&section=5" title="Редактиране на раздел: Отрицателни степенни показатели" class="mw-editsection-visualeditor"><span>редактиране</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%83%D0%B2%D0%B0%D0%BD%D0%B5_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)&action=edit&section=5" title="Edit section's source code: Отрицателни степенни показатели"><span>редактиране на кода</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Отрицателният степенен показател показва, че базата е сложена от другата страна спрямо дробната черта и за да стане с положителна стойност, изразът трябва да се премести от другата страна. Например в израза <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;x^{-2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;x^{-2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/923b916e10917d5b2a3c780519c14d22030d4afc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.308ex; height:2.676ex;" alt="{\displaystyle \;x^{-2}}"></span> (<i>хикс на минус втора</i>) <i><b>x</b></i> е поставен в числителя <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;{\frac {x^{-2}}{1}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> <mn>1</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;{\frac {x^{-2}}{1}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbc4e99a580ac1c59262ccba0d2ac5f486d826d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:5.144ex; height:5.676ex;" alt="{\displaystyle \;{\frac {x^{-2}}{1}}}"></span> вместо в знаменателя, което е равно на <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;{\frac {1}{(x)^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;{\frac {1}{(x)^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/330be1da3a0f595693d403782fcc6986722c8dd6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:5.675ex; height:6.009ex;" alt="{\displaystyle \;{\frac {1}{(x)^{2}}}}"></span>. </p><p>Още няколко примера, превръщащи отрицателната степен в положително число: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;x^{-4}={\frac {1x^{-4}}{1}}={\frac {1}{x^{4}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>4</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>4</mn> </mrow> </msup> </mrow> <mn>1</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;x^{-4}={\frac {1x^{-4}}{1}}={\frac {1}{x^{4}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/73da222884e53833e2f631d4734bdc1494fff4a7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:19.386ex; height:6.009ex;" alt="{\displaystyle \;x^{-4}={\frac {1x^{-4}}{1}}={\frac {1}{x^{4}}}}"></span><br /><br /></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;{\frac {x^{2}}{x^{-3}}}={\frac {1x^{2}}{1x^{-3}}}={\frac {1x^{2}x^{3}}{1}}=x^{5}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>1</mn> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> <mn>1</mn> </mfrac> </mrow> <mo>=</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;{\frac {x^{2}}{x^{-3}}}={\frac {1x^{2}}{1x^{-3}}}={\frac {1x^{2}x^{3}}{1}}=x^{5}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/263d942df66825cae3380cb9e9ba4eb52365028d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:29.251ex; height:6.009ex;" alt="{\displaystyle \;{\frac {x^{2}}{x^{-3}}}={\frac {1x^{2}}{1x^{-3}}}={\frac {1x^{2}x^{3}}{1}}=x^{5}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;2x^{-1}={\frac {2x^{-1}}{1}}={\frac {2}{x^{1}}}={\frac {2}{x}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <mn>2</mn> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mn>1</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2</mn> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2</mn> <mi>x</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;2x^{-1}={\frac {2x^{-1}}{1}}={\frac {2}{x^{1}}}={\frac {2}{x}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0dee910604a0cf26cc98d0d01b32aaac688dfe2d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:25.812ex; height:6.009ex;" alt="{\displaystyle \;2x^{-1}={\frac {2x^{-1}}{1}}={\frac {2}{x^{1}}}={\frac {2}{x}}}"></span><br /></dd></dl> <p>Забележете, че множителят 2 не се мести заедно с променливата <i>x</i>.<br /><br /> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;(3x)^{-2}={\frac {(3x)^{-2}}{1}}={\frac {1}{(3x)^{2}}}={\frac {1}{9x^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <mo stretchy="false">(</mo> <mn>3</mn> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mn>3</mn> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> <mn>1</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mo stretchy="false">(</mo> <mn>3</mn> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>9</mn> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;(3x)^{-2}={\frac {(3x)^{-2}}{1}}={\frac {1}{(3x)^{2}}}={\frac {1}{9x^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7adc4db08a70f68f8d555916479712d27c4c0f0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:34.619ex; height:6.676ex;" alt="{\displaystyle \;(3x)^{-2}={\frac {(3x)^{-2}}{1}}={\frac {1}{(3x)^{2}}}={\frac {1}{9x^{2}}}}"></span></dd></dl> <p>За разлика от предния пример, тук скобите показват, че отрицателната степен трябва да се приложи и върху числото 3 в скобите, както и върху променливата. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;{\left({\frac {x^{-2}}{y^{-3}}}\right)}^{-2}={\frac {(x^{-2})^{-2}}{(y^{-3})^{-2}}}={\frac {(y^{-3})^{2}}{(x^{-2})^{2}}}={\frac {y^{-6}}{x^{-4}}}={\frac {x^{4}}{y^{6}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mo stretchy="false">(</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>3</mn> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>3</mn> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>6</mn> </mrow> </msup> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>4</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;{\left({\frac {x^{-2}}{y^{-3}}}\right)}^{-2}={\frac {(x^{-2})^{-2}}{(y^{-3})^{-2}}}={\frac {(y^{-3})^{2}}{(x^{-2})^{2}}}={\frac {y^{-6}}{x^{-4}}}={\frac {x^{4}}{y^{6}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2f2ee7b8e42dd598e892eaf1991fff9e8c5a4d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:47.013ex; height:6.843ex;" alt="{\displaystyle \;{\left({\frac {x^{-2}}{y^{-3}}}\right)}^{-2}={\frac {(x^{-2})^{-2}}{(y^{-3})^{-2}}}={\frac {(y^{-3})^{2}}{(x^{-2})^{2}}}={\frac {y^{-6}}{x^{-4}}}={\frac {x^{4}}{y^{6}}}}"></span></dd></dl> <p>Същото може да се реши и така: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;{\left({\frac {x^{-2}}{y^{-3}}}\right)}^{-2}={\frac {(x^{-2})^{-2}}{(y^{-3})^{-2}}}={\frac {x^{4}}{y^{6}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mo stretchy="false">(</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>3</mn> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;{\left({\frac {x^{-2}}{y^{-3}}}\right)}^{-2}={\frac {(x^{-2})^{-2}}{(y^{-3})^{-2}}}={\frac {x^{4}}{y^{6}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ff9e77e91cbe94af88829f09447663ca013b1b3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:28.955ex; height:6.843ex;" alt="{\displaystyle \;{\left({\frac {x^{-2}}{y^{-3}}}\right)}^{-2}={\frac {(x^{-2})^{-2}}{(y^{-3})^{-2}}}={\frac {x^{4}}{y^{6}}}}"></span></dd></dl> <p>Тъй като степените означават умножение, а при умножение редът на множителите е без значение, често има повече от един начин за валидно опростяване на даден израз. Начинът е без значение стига стъпките да са правилни и да водят до един и същи отговор. </p> <div class="mw-heading mw-heading2"><h2 id="Дробни_(рационални)_степени"><span id=".D0.94.D1.80.D0.BE.D0.B1.D0.BD.D0.B8_.28.D1.80.D0.B0.D1.86.D0.B8.D0.BE.D0.BD.D0.B0.D0.BB.D0.BD.D0.B8.29_.D1.81.D1.82.D0.B5.D0.BF.D0.B5.D0.BD.D0.B8"></span>Дробни (рационални) степени</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%83%D0%B2%D0%B0%D0%BD%D0%B5_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)&veaction=edit&section=6" title="Редактиране на раздел: Дробни (рационални) степени" class="mw-editsection-visualeditor"><span>редактиране</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%83%D0%B2%D0%B0%D0%BD%D0%B5_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)&action=edit&section=6" title="Edit section's source code: Дробни (рационални) степени"><span>редактиране на кода</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/%D0%94%D1%80%D0%BE%D0%B1_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Дроб (математика)">Дробно число</a>, използвано за степенен показател се ползва и при обратното действие на степенуване – <a href="/wiki/%D0%9A%D0%BE%D1%80%D0%B5%D0%BD%D1%83%D0%B2%D0%B0%D0%BD%D0%B5" title="Коренуване">коренуване</a>, като <a href="/wiki/%D0%A7%D0%B8%D1%81%D0%BB%D0%B8%D1%82%D0%B5%D0%BB" class="mw-redirect" title="Числител">числителят</a> е степенният показател, а <a href="/wiki/%D0%97%D0%BD%D0%B0%D0%BC%D0%B5%D0%BD%D0%B0%D1%82%D0%B5%D0%BB" class="mw-redirect" title="Знаменател">знаменателят</a> е коренът, например: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;7^{\frac {2}{3}}={\sqrt[{3}]{7}}^{2}=({\sqrt[{3}]{7}})^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <msup> <mn>7</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> </mrow> </msup> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mn>7</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mroot> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mn>7</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mroot> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;7^{\frac {2}{3}}={\sqrt[{3}]{7}}^{2}=({\sqrt[{3}]{7}})^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3a8ea0690d074ec86dc59d841f7dbfda1c0ba7bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.855ex; height:4.009ex;" alt="{\displaystyle \;7^{\frac {2}{3}}={\sqrt[{3}]{7}}^{2}=({\sqrt[{3}]{7}})^{2}}"></span></dd></dl> <p>Еднаквите стойности на корен и степенен показател се анулират един друг и резултатът не се променя. Например: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;{\sqrt[{3}]{2^{3}}}=2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mroot> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mroot> </mrow> <mo>=</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;{\sqrt[{3}]{2^{3}}}=2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9101a09c9b1e2d0e619ad05fc58bd1ef3c3e9b56" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.447ex; height:3.509ex;" alt="{\displaystyle \;{\sqrt[{3}]{2^{3}}}=2}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;{\sqrt[{4}]{3^{4}}}=3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mroot> <msup> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mroot> </mrow> <mo>=</mo> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;{\sqrt[{4}]{3^{4}}}=3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6ecd86b0ee55e364089487a5f50a603df4ead7fe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.447ex; height:3.343ex;" alt="{\displaystyle \;{\sqrt[{4}]{3^{4}}}=3}"></span></dd></dl> <p>Освен тази има и още една зависимост (която между другото прави изчисления подобни на горното много по-лесни): <b>корен квадратен</b> или <b>корен втори</b> от дадено число може да се представи като степенуване с <a href="/wiki/%D0%A0%D0%B5%D1%86%D0%B8%D0%BF%D1%80%D0%BE%D1%87%D0%BD%D0%B0_%D1%81%D1%82%D0%BE%D0%B9%D0%BD%D0%BE%D1%81%D1%82" title="Реципрочна стойност">реципрочна стойност</a>. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;{\sqrt {2}}=2^{\frac {1}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <mo>=</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;{\sqrt {2}}=2^{\frac {1}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77aaf0ed47df978bd12e8b642518f63104d9a865" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.74ex; height:3.843ex;" alt="{\displaystyle \;{\sqrt {2}}=2^{\frac {1}{2}}}"></span><br /></dd></dl> <p>или </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;{\sqrt {4}}=4^{\frac {1}{2}}=2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>4</mn> </msqrt> </mrow> <mo>=</mo> <msup> <mn>4</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mo>=</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;{\sqrt {4}}=4^{\frac {1}{2}}=2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3e9d96da61380f514bb74dd2d6b07dd9bb7d2c37" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.001ex; height:3.843ex;" alt="{\displaystyle \;{\sqrt {4}}=4^{\frac {1}{2}}=2}"></span></dd></dl> <p>Съответно корен 3 и 4 и т.н. стават: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;{\sqrt[{3}]{8}}=8^{\frac {1}{3}}=2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mn>8</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mroot> </mrow> <mo>=</mo> <msup> <mn>8</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> </mrow> </msup> <mo>=</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;{\sqrt[{3}]{8}}=8^{\frac {1}{3}}=2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1a5867e998258f3cddd56805f1203fe096a5427" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.001ex; height:3.843ex;" alt="{\displaystyle \;{\sqrt[{3}]{8}}=8^{\frac {1}{3}}=2}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;{\sqrt[{4}]{81}}=81^{\frac {1}{4}}=3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mn>81</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mroot> </mrow> <mo>=</mo> <msup> <mn>81</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> </msup> <mo>=</mo> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;{\sqrt[{4}]{81}}=81^{\frac {1}{4}}=3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cfaa0eee9ef9c4d0ffe706a0a3f674236426fc76" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:16.326ex; height:3.843ex;" alt="{\displaystyle \;{\sqrt[{4}]{81}}=81^{\frac {1}{4}}=3}"></span></dd></dl> <p>Така горните примери можем да запишем по следния начин: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;{\sqrt[{3}]{2^{3}}}={(2^{3})}^{\frac {1}{3}}={(2^{\frac {3}{1}})^{\frac {1}{3}}}=2^{{\frac {3}{1}}\times {\frac {1}{3}}}=2^{1}=2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mroot> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mroot> </mrow> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>1</mn> </mfrac> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> </mrow> </msup> </mrow> <mo>=</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>1</mn> </mfrac> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> </mrow> </mrow> </msup> <mo>=</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msup> <mo>=</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;{\sqrt[{3}]{2^{3}}}={(2^{3})}^{\frac {1}{3}}={(2^{\frac {3}{1}})^{\frac {1}{3}}}=2^{{\frac {3}{1}}\times {\frac {1}{3}}}=2^{1}=2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4112969fa8d634681e6c842acf97753f547b7ea6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:41.942ex; height:4.343ex;" alt="{\displaystyle \;{\sqrt[{3}]{2^{3}}}={(2^{3})}^{\frac {1}{3}}={(2^{\frac {3}{1}})^{\frac {1}{3}}}=2^{{\frac {3}{1}}\times {\frac {1}{3}}}=2^{1}=2}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;{\sqrt[{4}]{(3)^{4}}}=(3^{4})^{\frac {1}{4}}=(3^{\frac {4}{1}})^{\frac {1}{4}}=3^{{\frac {4}{1}}\times {\frac {1}{4}}}=3^{1}=3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mrow> <mo stretchy="false">(</mo> <mn>3</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </mroot> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <msup> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <msup> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>4</mn> <mn>1</mn> </mfrac> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> </msup> <mo>=</mo> <msup> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>4</mn> <mn>1</mn> </mfrac> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> </mrow> </msup> <mo>=</mo> <msup> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msup> <mo>=</mo> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;{\sqrt[{4}]{(3)^{4}}}=(3^{4})^{\frac {1}{4}}=(3^{\frac {4}{1}})^{\frac {1}{4}}=3^{{\frac {4}{1}}\times {\frac {1}{4}}}=3^{1}=3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99829c97ddbf29c48e948ca530f838cad5103bc9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:43.751ex; height:4.843ex;" alt="{\displaystyle \;{\sqrt[{4}]{(3)^{4}}}=(3^{4})^{\frac {1}{4}}=(3^{\frac {4}{1}})^{\frac {1}{4}}=3^{{\frac {4}{1}}\times {\frac {1}{4}}}=3^{1}=3}"></span></dd></dl> <p>Ако се използва калкулатор, дробният степенен показател трябва да се сложи в скоби, напр. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;15^{\frac {4}{5}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <msup> <mn>15</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>4</mn> <mn>5</mn> </mfrac> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;15^{\frac {4}{5}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/501fbe2ea181de24e904676f3b12a86f2b98bd29" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.706ex; height:3.509ex;" alt="{\displaystyle \;15^{\frac {4}{5}}}"></span> трябва да стане <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;15^{(4/5)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <msup> <mn>15</mn> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>4</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>5</mn> <mo stretchy="false">)</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;15^{(4/5)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6761f8cb50b5e4bb6dff1ceab4259bf248a41105" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.948ex; height:2.843ex;" alt="{\displaystyle \;15^{(4/5)}}"></span>, защото иначе калкулаторът ще приеме, че е въведено <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;(15^{4})\div 5}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <mo stretchy="false">(</mo> <msup> <mn>15</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo>÷</mo> <mn>5</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;(15^{4})\div 5}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/982c855ac7b31ee8e166b42ddfa4197f79f07871" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.836ex; height:3.176ex;" alt="{\displaystyle \;(15^{4})\div 5}"></span>. </p><p>Дробните степени позволяват по-голяма гъвкавост (което може да се види при много изчисления) и е по-лесно да се запише отколкото еквивалентния формат, като позволява изчисления, които иначе са невъзможни. Например: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;({\sqrt[{10}]{2}}5)^{5}=(25^{\frac {1}{10}})^{5}=25^{{\frac {1}{10}}\times {\frac {5}{1}}}=25^{\frac {1}{2}}={\sqrt {2}}5=5}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </mroot> </mrow> <mn>5</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <msup> <mn>25</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>10</mn> </mfrac> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <mo>=</mo> <msup> <mn>25</mn> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>10</mn> </mfrac> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>5</mn> <mn>1</mn> </mfrac> </mrow> </mrow> </msup> <mo>=</mo> <msup> <mn>25</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <mn>5</mn> <mo>=</mo> <mn>5</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;({\sqrt[{10}]{2}}5)^{5}=(25^{\frac {1}{10}})^{5}=25^{{\frac {1}{10}}\times {\frac {5}{1}}}=25^{\frac {1}{2}}={\sqrt {2}}5=5}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0bdfaa14efd1285166eee9fc2eb0899f8b53dfef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:47.87ex; height:4.009ex;" alt="{\displaystyle \;({\sqrt[{10}]{2}}5)^{5}=(25^{\frac {1}{10}})^{5}=25^{{\frac {1}{10}}\times {\frac {5}{1}}}=25^{\frac {1}{2}}={\sqrt {2}}5=5}"></span></dd></dl> <p>Някои степени под формата на десетична дроб, могат да се пренапишат така, че да станат обикновена дроб: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;3^{5,5}=3^{\frac {11}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <msup> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> <mo>,</mo> <mn>5</mn> </mrow> </msup> <mo>=</mo> <msup> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>11</mn> <mn>2</mn> </mfrac> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;3^{5,5}=3^{\frac {11}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cee28b85ef68ea8778238d88d13c239c0c2b2188" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.805ex; height:3.509ex;" alt="{\displaystyle \;3^{5,5}=3^{\frac {11}{2}}}"></span></dd></dl> <p>Като цяло обаче при десетичната степенна дроб (нещо различно от обикновена дроб или цяло число), трябва да го оставим така както е или ако е необходимо да го изчислим с калкулатор. 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