{"id":11019,"date":"2012-10-26T14:38:14","date_gmt":"2012-10-26T13:38:14","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=11019"},"modified":"2022-01-02T01:10:45","modified_gmt":"2022-01-02T01:10:45","slug":"calcula-utilizando-as-regras-das-potencias","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=11019","title":{"rendered":"Calcula utilizando as regras das pot\u00eancias"},"content":{"rendered":"<p><ul id='GTTabs_ul_11019' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_11019' class='GTTabs_curr'><a  id=\"11019_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_11019' ><a  id=\"11019_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_11019'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Calcula o valor de cada express\u00e3o num\u00e9rica, utilizando as regras operat\u00f3rias das pot\u00eancias:<\/p>\n<ol>\n<li>\u00a0${\\left( { &#8211; 3} \\right)^2} \\times {\\left( { &#8211; 3} \\right)^5}$<\/li>\n<li>${\\left( {{2^2}} \\right)^3} \\times {\\left( { &#8211; 3} \\right)^6}$<\/li>\n<li>${\\left( { &#8211; 2} \\right)^4} \\times {\\left( { + 3} \\right)^4}$<\/li>\n<li>${\\left( { &#8211; 5} \\right)^3} \\times \\left( { &#8211; 5} \\right)$<\/li>\n<li>${\\left( { &#8211; 5} \\right)^8} \\div {\\left( { &#8211; 5} \\right)^7}$<\/li>\n<li>${15^2} \\div {3^2}$<\/li>\n<li>${63^5} \\div {\\left( { &#8211; 7} \\right)^5}$<\/li>\n<li>${\\left( { &#8211; 3} \\right)^6} \\div \\left( { &#8211; 3} \\right)$<\/li>\n<li>${6^7} \\div {\\left( { &#8211; 6} \\right)^4}$<\/li>\n<li>${14^2} \\div {2^2}$<\/li>\n<li>${2^3} \\times {\\left( { &#8211; 3} \\right)^3}$<\/li>\n<li>${\\left( { &#8211; 2} \\right)^2} \\times {\\left( { &#8211; 2} \\right)^3}$<\/li>\n<li>${\\left( { &#8211; 7} \\right)^2} \\div {\\left( { &#8211; 1} \\right)^2}$<\/li>\n<li>${\\left( 5 \\right)^{11}} \\div {\\left( {{5^4}} \\right)^2}$<\/li>\n<li>${3^2} \\times {5^2}$<\/li>\n<li>${\\left( { &#8211; 1} \\right)^5} \\times {2^5}$<\/li>\n<li>${\\left( { &#8211; 1} \\right)^4} \\times {3^4}$<\/li>\n<li>${2^2} \\times {\\left( { &#8211; 2} \\right)^3}$<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_11019' onClick='GTTabs_show(1,11019)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_11019'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Ora,<br \/>\n$\\begin{array}{*{20}{l}} \u00a0 {{{\\left( { &#8211; 3} \\right)}^2} \\times {{\\left( { &#8211; 3} \\right)}^5}}&amp; = &amp;{{{\\left( { &#8211; 3} \\right)}^7}} \\\\ \u00a0 {}&amp; = &amp;{ &#8211; 2187} \\end{array}$<\/li>\n<li>Ora,<br \/>\n$\\begin{array}{*{20}{l}} \u00a0 {{{\\left( {{2^2}} \\right)}^3} \\times {{\\left( { &#8211; 3} \\right)}^6}}&amp; = &amp;{{2^6} \\times {{\\left( { &#8211; 3} \\right)}^6}} \\\\ \u00a0 {}&amp; = &amp;{{{\\left( { &#8211; 6} \\right)}^6}} \\\\ \u00a0 {}&amp; = &amp;{46656} \\end{array}$<\/li>\n<li>Ora,<br \/>\n$\\begin{array}{*{20}{l}} \u00a0 {{{\\left( { &#8211; 2} \\right)}^4} \\times {{\\left( { + 3} \\right)}^4}}&amp; = &amp;{{{\\left( { &#8211; 6} \\right)}^4}} \\\\ \u00a0 {}&amp; = &amp;{1296} \\end{array}$<\/li>\n<li>Ora,<br \/>\n$\\begin{array}{*{20}{l}} \u00a0 {{{\\left( { &#8211; 5} \\right)}^3} \\times \\left( { &#8211; 5} \\right)}&amp; = &amp;{{{\\left( { &#8211; 5} \\right)}^3} \\times {{\\left( { &#8211; 5} \\right)}^1}} \\\\ \u00a0 {}&amp; = &amp;{{{\\left( { &#8211; 5} \\right)}^4}} \\\\ \u00a0 {}&amp; = &amp;{625} \\end{array}$<\/li>\n<li>\u00a0Ora,<br \/>\n$\\begin{array}{*{20}{l}} \u00a0 {{{\\left( { &#8211; 5} \\right)}^8} \\div {{\\left( { &#8211; 5} \\right)}^7}}&amp; = &amp;{{{\\left( { &#8211; 5} \\right)}^1}} \\\\ \u00a0 {}&amp; = &amp;{ &#8211; 5} \\end{array}$<\/li>\n<li>Ora,<br \/>\n$\\begin{array}{*{20}{l}} \u00a0 {{{15}^2} \\div {3^2}}&amp; = &amp;{{5^2}} \\\\ \u00a0 {}&amp; = &amp;{25} \\end{array}$<\/li>\n<li>Ora,<br \/>\n$\\begin{array}{*{20}{l}} \u00a0 {{{63}^5} \\div {{\\left( { &#8211; 7} \\right)}^5}}&amp; = &amp;{{{\\left( { &#8211; 9} \\right)}^5}} \\\\ \u00a0 {}&amp; = &amp;{ &#8211; 59049} \\end{array}$<\/li>\n<li>Ora,<br \/>\n$\\begin{array}{*{20}{l}} \u00a0 {{{\\left( { &#8211; 3} \\right)}^6} \\div \\left( { &#8211; 3} \\right)}&amp; = &amp;{{{\\left( { &#8211; 3} \\right)}^6} \\div {{\\left( { &#8211; 3} \\right)}^{ &#8211; 1}}} \\\\ \u00a0 {}&amp; = &amp;{{{\\left( { &#8211; 3} \\right)}^5}} \\\\ \u00a0 {}&amp; = &amp;{ &#8211; 243} \\end{array}$<\/li>\n<li>As pot\u00eancias n\u00e3o possuem bases iguais nem expoentes iguais, pelo que n\u00e3o h\u00e1 regra operat\u00f3ria para esta situa\u00e7\u00e3o. No entanto, como ${\\left( { &#8211; 6} \\right)^4} = {\\left( { + 6} \\right)^4}$, temos:\n<p>$\\begin{array}{*{20}{l}} \u00a0 {{6^7} \\div {{\\left( { &#8211; 6} \\right)}^4}}&amp; = &amp;{{6^7} \\div {{\\left( { + 6} \\right)}^4}} \\\\ \u00a0 {}&amp; = &amp;{{6^3}} \\\\ \u00a0 {}&amp; = &amp;{216} \\end{array}$<\/p>\n<\/li>\n<li>Ora,<br \/>\n$\\begin{array}{*{20}{l}} \u00a0 {{{14}^2} \\div {2^2}}&amp; = &amp;{{7^2}} \\\\ \u00a0 {}&amp; = &amp;{49} \\end{array}$<\/li>\n<li>Ora,<br \/>\n$\\begin{array}{*{20}{l}} \u00a0 {{2^3} \\times {{\\left( { &#8211; 3} \\right)}^3}}&amp; = &amp;{{{\\left( { &#8211; 6} \\right)}^3}} \\\\ \u00a0 {}&amp; = &amp;{ &#8211; 216} \\end{array}$<\/li>\n<li>Ora,<br \/>\n$\\begin{array}{*{20}{l}} \u00a0 {{{\\left( { &#8211; 2} \\right)}^2} \\times {{\\left( { &#8211; 2} \\right)}^3}}&amp; = &amp;{{{\\left( { &#8211; 2} \\right)}^5}} \\\\ \u00a0 {}&amp; = &amp;{ &#8211; 32} \\end{array}$<\/li>\n<li>Ora,<br \/>\n$\\begin{array}{*{20}{l}} \u00a0 {{{\\left( { &#8211; 7} \\right)}^2} \\div {{\\left( { &#8211; 1} \\right)}^2}}&amp; = &amp;{{7^2}} \\\\ \u00a0 {}&amp; = &amp;{49} \\end{array}$<\/li>\n<li>Ora,<br \/>\n$\\begin{array}{*{20}{l}} \u00a0 {{{\\left( 5 \\right)}^{11}} \\div {{\\left( {{5^4}} \\right)}^2}}&amp; = &amp;{{5^{11}} \\div {5^8}} \\\\ \u00a0 {}&amp; = &amp;{{5^3}} \\\\ \u00a0 {}&amp; = &amp;{125} \\end{array}$<\/li>\n<li>Ora,<br \/>\n$\\begin{array}{*{20}{l}} \u00a0 {{3^2} \\times {5^2}}&amp; = &amp;{{{15}^2}} \\\\ \u00a0 {}&amp; = &amp;{225} \\end{array}$<\/li>\n<li>Ora,<br \/>\n$\\begin{array}{*{20}{l}} \u00a0 {{{\\left( { &#8211; 1} \\right)}^5} \\times {2^5}}&amp; = &amp;{{{\\left( { &#8211; 2} \\right)}^5}} \\\\ \u00a0 {}&amp; = &amp;{ &#8211; 32} \\end{array}$<\/li>\n<li>Ora,<br \/>\n$\\begin{array}{*{20}{l}} \u00a0 {{{\\left( { &#8211; 1} \\right)}^4} \\times {3^4}}&amp; = &amp;{{{\\left( { &#8211; 3} \\right)}^4}} \\\\ \u00a0 {}&amp; = &amp;{81} \\end{array}$<\/li>\n<li>As pot\u00eancias n\u00e3o possuem bases iguais nem expoentes iguais, pelo que n\u00e3o h\u00e1 regra operat\u00f3ria para esta situa\u00e7\u00e3o. No entanto, como ${2^2} = {\\left( { &#8211; 2} \\right)^2}$, temos:\n<p>$\\begin{array}{*{20}{l}} \u00a0 {{2^2} \\times {{\\left( { &#8211; 2} \\right)}^3}}&amp; = &amp;{{{\\left( { &#8211; 2} \\right)}^2} \\times {{\\left( { &#8211; 2} \\right)}^3}} \\\\ \u00a0 {}&amp; = &amp;{{{\\left( { &#8211; 2} \\right)}^5}} \\\\ \u00a0 {}&amp; = &amp;{ &#8211; 32} \\end{array}$<\/p>\n<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_11019' onClick='GTTabs_show(0,11019)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Calcula o valor de cada express\u00e3o num\u00e9rica, utilizando as regras operat\u00f3rias das pot\u00eancias: \u00a0${\\left( { &#8211; 3} \\right)^2} \\times {\\left( { &#8211; 3} \\right)^5}$ ${\\left( {{2^2}} \\right)^3} \\times {\\left( { &#8211;&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14083,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[317,97,318],"tags":[428,319,142,337],"series":[],"class_list":["post-11019","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-7-o-ano","category-aplicando","category-numeros-inteiros","tag-7-o-ano","tag-numeros-inteiros-2","tag-potencias","tag-regras-operatorias-de-potencias"],"views":1572,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat28.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11019","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=11019"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11019\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11019"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11019"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11019"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=11019"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}