{"id":94653,"date":"2017-01-12T16:03:25","date_gmt":"2017-01-12T18:03:25","guid":{"rendered":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/?p=94653"},"modified":"2017-01-12T18:09:27","modified_gmt":"2017-01-12T20:09:27","slug":"radiciacao-e-potenciacao","status":"publish","type":"post","link":"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/matematica\/radiciacao-e-potenciacao","title":{"rendered":"Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o"},"content":{"rendered":"<h2>Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o<\/h2>\n<h3>Defini\u00e7\u00e3o de Potencia\u00e7\u00e3o<\/h3>\n<p>A potencia\u00e7\u00e3o indica multiplica\u00e7\u00f5es de fatores iguais. Por exemplo, o produto 3.3.3.3 pode ser indicado na forma 3<sup>4<\/sup> . Assim, o s\u00edmbolo , sendo <em>a<sup>n<\/sup><\/em> um n\u00famero inteiro e <em>n<\/em> um n\u00famero natural maior que 1, significa o produto de <em>n<\/em> fatores iguais a <em>a<\/em>:<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-94660\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_56-Jan.-12-15.25.jpg\" alt=\"Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o\" width=\"142\" height=\"45\" \/><\/p>\n<ul>\n<li><em>a <\/em>\u00e9 a <strong>base<\/strong>;<\/li>\n<li><em>n<\/em> \u00e9 o <strong>expoente<\/strong>;<\/li>\n<li>o resultado \u00e9 a <strong>pot\u00eancia<\/strong><em>.<\/em><\/li>\n<\/ul>\n<p>Por defini\u00e7\u00e3o temos que:<img decoding=\"async\" class=\"aligncenter size-full wp-image-94665\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_60-Jan.-12-15.29.jpg\" alt=\"Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o\" width=\"130\" height=\"26\" \/><\/p>\n<p>Exemplos:<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-94666\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_59-Jan.-12-15.281.jpg\" alt=\"Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o\" width=\"249\" height=\"130\" \/><\/p>\n<p><strong><em>Cuidado com os sinais.<\/em><\/strong><\/p>\n<ul>\n<li><strong><em>N\u00famero negativo elevado a expoente par fica <u>positivo<\/u>. Exemplos:<\/em><\/strong><\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-medium wp-image-94671\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_61-Jan.-12-15.31-300x48.jpg\" alt=\"Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o\" width=\"300\" height=\"48\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_61-Jan.-12-15.31-300x48.jpg 300w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_61-Jan.-12-15.31.jpg 310w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<ul>\n<li><strong><em>N\u00famero negativo elevado a expoente \u00edmpar permanece negativo. Exemplo:<\/em><\/strong><\/li>\n<\/ul>\n<p><strong><em>Ex. 1: <\/em><\/strong><strong><em>\u00a0\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-94673 size-full\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_62-Jan.-12-15.32.jpg\" alt=\"Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o\" width=\"651\" height=\"195\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_62-Jan.-12-15.32.jpg 651w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_62-Jan.-12-15.32-300x90.jpg 300w\" sizes=\"(max-width: 651px) 100vw, 651px\" \/> <\/em><\/strong><\/p>\n<p><strong><em>\u00a0Propriedades da Potencia\u00e7\u00e3o<\/em><\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-94676 size-full\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_63-Jan.-12-15.34.jpg\" alt=\"Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o\" width=\"694\" height=\"220\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_63-Jan.-12-15.34.jpg 694w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_63-Jan.-12-15.34-300x95.jpg 300w\" sizes=\"(max-width: 694px) 100vw, 694px\" \/><\/p>\n<p>A seguir apresentamos alguns exemplos para ilustrar o uso das propriedades:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-94680\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_64-Jan.-12-15.35.jpg\" alt=\"Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o\" width=\"129\" height=\"31\" \/><\/p>\n<ol>\n<li>Nesta propriedade vemos que quando tivermos multiplica\u00e7\u00e3o de potencias de bases iguais temos que conservar a base e somar os expoentes.<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-94684\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_65-Jan.-12-15.37.jpg\" alt=\"Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o\" width=\"221\" height=\"49\" \/><\/li>\n<\/ol>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-94687 alignnone\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_66-Jan.-12-15.37.jpg\" alt=\"Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o\" width=\"124\" height=\"23\" \/>neste caso devemos primeiramente resolver as pot\u00eancias para depois multiplicar os resultados, pois as bases 4 e 3 s\u00e3o diferentes.<\/p>\n<p><strong><em>Obs.:\u00a0\u00a0 Devemos lembrar que esta propriedade \u00e9 v\u00e1lida nos dois sentidos. <\/em><\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-94690 size-full\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_69-Jan.-12-15.39.jpg\" alt=\"Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o\" width=\"553\" height=\"46\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_69-Jan.-12-15.39.jpg 553w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_69-Jan.-12-15.39-300x25.jpg 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-94693 alignnone\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_71-Jan.-12-15.41.jpg\" alt=\"Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o\" width=\"104\" height=\"49\" \/>Nesta propriedade vemos que quando tivermos divis\u00e3o de potencias de bases iguais temos que conservar a base e subtrair\u00a0 os expoentes.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-94697\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_72-Jan.-12-15.42.jpg\" alt=\"Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o\" width=\"203\" height=\"101\" \/><\/p>\n<p><strong><em>Esta propriedade tamb\u00e9m \u00e9 v\u00e1lida nos dois sentidos, ou seja<\/em><\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-94698 size-full\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_73-Jan.-12-15.43.jpg\" alt=\"Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o\" width=\"420\" height=\"65\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_73-Jan.-12-15.43.jpg 420w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_73-Jan.-12-15.43-300x46.jpg 300w\" sizes=\"(max-width: 420px) 100vw, 420px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-94700 alignnone\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_74-Jan.-12-15.44.jpg\" alt=\"Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o\" width=\"116\" height=\"38\" \/>Nesta propriedade temos uma\u00a0 potencia\u00a0 elevada a um outro expoente, para resolver temos que conservar a base e multiplicar os expoentes.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-94705\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_78-Jan.-12-15.45.jpg\" alt=\"Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o\" width=\"217\" height=\"60\" \/><\/p>\n<p><strong><em>Obs.:Esta propriedade tamb\u00e9m \u00e9 v\u00e1lida nos dois sentidos, ou seja<\/em><\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-94701 size-full\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_75-Jan.-12-15.44.jpg\" alt=\"Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o\" width=\"499\" height=\"43\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_75-Jan.-12-15.44.jpg 499w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_75-Jan.-12-15.44-300x26.jpg 300w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-94702 alignnone\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_76-Jan.-12-15.44.jpg\" alt=\"Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o\" width=\"110\" height=\"36\" \/>Esta propriedade nos mostra que todo radical pode se transformado numa potencia de expoente fracion\u00e1rio, onde o \u00edndice da raiz \u00e9 o denominador do expoente.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-94703 size-full\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_77-Jan.-12-15.44.jpg\" alt=\"Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o\" width=\"210\" height=\"119\" \/><\/p>\n<p><strong><em>Obs.:Esta propriedade tamb\u00e9m \u00e9 v\u00e1lida nos dois sentidos, ou seja<\/em><\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-94707 size-full\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_79-Jan.-12-15.48.jpg\" alt=\"Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o\" width=\"470\" height=\"44\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_79-Jan.-12-15.48.jpg 470w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_79-Jan.-12-15.48-300x28.jpg 300w\" sizes=\"(max-width: 470px) 100vw, 470px\" \/><\/p>\n<h3>Defini\u00e7\u00e3o de Radicia\u00e7\u00e3o<\/h3>\n<p>A radicia\u00e7\u00e3o \u00e9 a opera\u00e7\u00e3o inversa da potencia\u00e7\u00e3o. De modo geral podemos escrever:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-94713 size-full\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_81-Jan.-12-15.50.jpg\" alt=\"Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o\" width=\"357\" height=\"33\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_81-Jan.-12-15.50.jpg 357w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_81-Jan.-12-15.50-300x28.jpg 300w\" sizes=\"(max-width: 357px) 100vw, 357px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-94714\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_82-Jan.-12-15.50.jpg\" alt=\"Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o\" width=\"283\" height=\"97\" \/><\/p>\n<ul>\n<li>O n\u00famero n \u00e9 chamado<strong> \u00edndice;<\/strong><\/li>\n<li>O n\u00famero a \u00e9 chamado<\/li>\n<\/ul>\n<h4>Propriedades dos radicais<\/h4>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-94718\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_83-Jan.-12-15.52.jpg\" alt=\"Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o\" width=\"146\" height=\"149\" \/><\/p>\n<p>Essa propriedade mostra que todo radical pode ser escrito na forma de uma pot\u00eancia.<\/p>\n<p><strong><em>Obs.: \u00e9 importante lembrar que esta propriedade tamb\u00e9m\u00a0 \u00e9 muito\u00a0 usada no sentido contr\u00e1rio ou seja (o denominador \u201cn\u201d do expoente fracion\u00e1rio \u00e9 o \u00edndice do radical).<\/em><\/strong><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-94726\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_84-Jan.-12-15.57.jpg\" alt=\"Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o\" width=\"75\" height=\"28\" \/><\/p>\n<p>Exemplo:<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-94733\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_86-Jan.-12-15.59.jpg\" alt=\"Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o\" width=\"66\" height=\"31\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-94749 size-full\" src=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_87-Jan.-12-16.23.jpg\" alt=\"Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o\" width=\"548\" height=\"365\" srcset=\"https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_87-Jan.-12-16.23.jpg 548w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_87-Jan.-12-16.23-300x200.jpg 300w, https:\/\/lab.fabricadelandings.com.br\/portalsaofrancisconovo\/wp-content\/uploads\/2017\/01\/ScreenHunter_87-Jan.-12-16.23-310x205.jpg 310w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o Defini\u00e7\u00e3o de Potencia\u00e7\u00e3o A potencia\u00e7\u00e3o indica multiplica\u00e7\u00f5es de fatores iguais. Por exemplo, o produto 3.3.3.3 pode ser indicado na forma 34 . Assim, o s\u00edmbolo , sendo an um n\u00famero inteiro e n um n\u00famero natural maior que 1, significa o produto de n fatores iguais a a: a \u00e9 a base; [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[414],"tags":[],"class_list":["post-94653","post","type-post","status-publish","format-standard","hentry","category-matematica"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o, Matem\u00e1tica Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o,<\/title>\n<meta name=\"description\" content=\"Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o, Matem\u00e1tica, Exemplos, Modelos, O que \u00e9 Radicia\u00e7\u00e3o e Potencia\u00e7\u00e3o\" \/>\n<meta name=\"robots\" content=\"noindex, 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