{"id":22637,"date":"2022-10-22T15:32:29","date_gmt":"2022-10-22T14:32:29","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=22637"},"modified":"2022-10-22T18:08:41","modified_gmt":"2022-10-22T17:08:41","slug":"e-igual-a","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=22637","title":{"rendered":"\u00c9 igual a"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_22637' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_22637' class='GTTabs_curr'><a  id=\"22637_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_22637' ><a  id=\"22637_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_22637'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>\\[{{{\\left[ {{3^2} \\times {{\\left( {{3^2} + 1} \\right)}^2} \\div {{\\left( { &#8211; 5} \\right)}^2}} \\right]}^{ &#8211; 2}} \\div {6^2} \\times {{\\left( { &#8211; \\frac{1}{3}} \\right)}^0}}\\]<\/p>\n<p>\u00e9 igual a:<\/p>\n<p><strong>[A]<\/strong> \\({\\left( { &#8211; 6} \\right)^6}\\)<\/p>\n<p><strong>[B]<\/strong> \\({6^{ &#8211; 6}}\\)<\/p>\n<p><strong>[C]<\/strong> \\({6^{ &#8211; 2}}\\)<\/p>\n<p><strong>[D]<\/strong> \\({\\left( { &#8211; 6} \\right)^{ &#8211; 2}}\\)<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_22637' onClick='GTTabs_show(1,22637)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_22637'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Aplicando, sempre que poss\u00edvel, as regras operat\u00f3rias das pot\u00eancias, temos:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{{\\left[ {{3^2} \\times {{\\left( {{3^2} + 1} \\right)}^2} \\div {{\\left( { &#8211; 5} \\right)}^2}} \\right]}^{ &#8211; 2}} \\div {6^2} \\times {{\\left( { &#8211; \\frac{1}{3}} \\right)}^0}}&amp; = &amp;{{{\\left[ {{{\\left( {3 \\times \\left( {{3^2} + 1} \\right)} \\right)}^2} \\div {{\\left( { &#8211; 5} \\right)}^2}} \\right]}^{ &#8211; 2}} \\div {6^2} \\times 1}&amp;{(1)}\\\\{}&amp; = &amp;{{{\\left[ {{{\\left( {\\frac{{3 \\times \\left( {{3^2} + 1} \\right)}}{{ &#8211; 5}}} \\right)}^2}} \\right]}^{ &#8211; 2}} \\div {6^2}}&amp;{(2)}\\\\{}&amp; = &amp;{{{\\left[ {{{\\left( {\\frac{{{3^3} + 3}}{{ &#8211; 5}}} \\right)}^2}} \\right]}^{ &#8211; 2}} \\div {6^2}}&amp;{(3)}\\\\{}&amp; = &amp;{{{\\left[ {{{\\left( { &#8211; 6} \\right)}^2}} \\right]}^{ &#8211; 2}} \\div {6^2}}&amp;{(4)}\\\\{}&amp; = &amp;{{{\\left( { + 6} \\right)}^{ &#8211; 4}} \\div {6^2}}&amp;{(5)}\\\\{}&amp; = &amp;{{6^{ &#8211; 6}}}&amp;{(6)}\\end{array}\\]<\/p>\n<p>Portanto, a op\u00e7\u00e3o correta \u00e9 <strong>[B]<\/strong>.<\/p>\n<p>\u00a0<\/p>\n<h6>Explica\u00e7\u00e3o e fundamento dos c\u00e1lculos efetuados:<\/h6>\n<table style=\"border-collapse: collapse;\">\n<tbody>\n<tr>\n<td rowspan=\"2\">(<strong>1<\/strong>)<\/td>\n<td style=\"text-align: left;\">Multiplica\u00e7\u00e3o de pot\u00eancias de igual expoente: \\({3^2} \\times {\\left( {{3^2} + 1} \\right)^2} = {\\left( {3 \\times \\left( {{3^2} + 1} \\right)} \\right)^2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: left;\">Reconhecimento de \\({\\left( { &#8211; \\frac{1}{3}} \\right)^0} = 1\\)<\/td>\n<\/tr>\n<tr>\n<td rowspan=\"2\">(<strong>2<\/strong>)<\/td>\n<td style=\"text-align: left;\">Divis\u00e3o de pot\u00eancias de igual expoente: \\({\\left( {3 \\times \\left( {{3^2} + 1} \\right)} \\right)^2} \\div {\\left( { &#8211; 5} \\right)^2} = {\\left( {\\frac{{3 \\times \\left( {{3^2} + 1} \\right)}}{{ &#8211; 5}}} \\right)^2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: left;\">Reconhecimento de que \\(1\\) \u00e9 o elemento neutro da multiplica\u00e7\u00e3o: \\({\\left[ { \\cdots \\quad \\cdots } \\right]^{ &#8211; 2}} \\div {6^2} \\times 1 = {\\left[ { \\cdots \\quad \\cdots } \\right]^{ &#8211; 2}} \\div {6^2}\\)<\/td>\n<\/tr>\n<tr>\n<td>(<strong>3<\/strong>)<\/td>\n<td style=\"text-align: left;\">Aplica\u00e7\u00e3o da propriedade distributiva da multiplica\u00e7\u00e3o em rela\u00e7\u00e3o \u00e0 adi\u00e7\u00e3o e<br \/>multiplica\u00e7\u00e3o de pot\u00eancias de igual base: \\(\\frac{{3 \\times \\left( {{3^2} + 1} \\right)}}{{ &#8211; 5}} = \\frac{{{3^3} + 3}}{{ &#8211; 5}}\\)<\/td>\n<\/tr>\n<tr>\n<td>(<strong>4<\/strong>)<\/td>\n<td style=\"text-align: left;\">Simplifica\u00e7\u00e3o da base da pot\u00eancia de pot\u00eancia: \\({\\left[ {{{\\left( {\\frac{{{3^3} + 3}}{{ &#8211; 5}}} \\right)}^2}} \\right]^{ &#8211; 2}} = {\\left[ {{{\\left( { &#8211; 6} \\right)}^2}} \\right]^{ &#8211; 2}}\\)<\/td>\n<\/tr>\n<tr>\n<td>(<strong>5<\/strong>)<\/td>\n<td style=\"text-align: left;\">Aplica\u00e7\u00e3o da regra da pot\u00eancia de pot\u00eancia e<br \/>reconhecimento de que \u00e9 positiva a pot\u00eancia de base negativa e expoente par: \\({\\left[ {{{\\left( { &#8211; 6} \\right)}^2}} \\right]^{ &#8211; 2}} = {\\left( { + 6} \\right)^{ &#8211; 4}}\\)<\/td>\n<\/tr>\n<tr>\n<td>(<strong>6<\/strong>)<\/td>\n<td style=\"text-align: left;\">Divis\u00e3o de pot\u00eancias de igual base: \\({\\left( { + 6} \\right)^{ &#8211; 4}} \\div {6^2} = {6^{ &#8211; 6}}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_22637' onClick='GTTabs_show(0,22637)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado \\[{{{\\left[ {{3^2} \\times {{\\left( {{3^2} + 1} \\right)}^2} \\div {{\\left( { &#8211; 5} \\right)}^2}} \\right]}^{ &#8211; 2}} \\div {6^2} \\times {{\\left( { &#8211; \\frac{1}{3}} \\right)}^0}}\\] \u00e9 igual a: [A] \\({\\left( {&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19172,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,258],"tags":[424,142,337],"series":[],"class_list":["post-22637","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-os-numeros-reais","tag-8-o-ano","tag-potencias","tag-regras-operatorias-de-potencias"],"views":368,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat63.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/22637","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=22637"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/22637\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19172"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=22637"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=22637"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=22637"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=22637"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}