{"id":22330,"date":"2022-10-16T21:20:51","date_gmt":"2022-10-16T20:20:51","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=22330"},"modified":"2022-10-17T21:28:03","modified_gmt":"2022-10-17T20:28:03","slug":"calcula-o-valor-das-expressoes-numericas","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=22330","title":{"rendered":"Calcula o valor das express\u00f5es num\u00e9ricas"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_22330' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_22330' class='GTTabs_curr'><a  id=\"22330_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_22330' ><a  id=\"22330_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_22330'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Calcula o valor das express\u00f5es num\u00e9ricas utilizando, sempre que poss\u00edvel, as regras de opera\u00e7\u00f5es com pot\u00eancias:<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 33.3333%; text-align: left;\">\n<ol style=\"list-style-type: lower-alpha;\">\n<li>\\({\\left( {{3^2}} \\right)^{ &#8211; 1}}\\)<\/li>\n<li>\\({\\left[ {{{\\left( {\\frac{3}{2}} \\right)}^2}} \\right]^0}\\)<\/li>\n<li>\\({\\left[ {{{\\left( { &#8211; 5} \\right)}^2}} \\right]^{ &#8211; 2}}\\)<\/li>\n<li>\\({\\left[ {{{\\left( { &#8211; 0,25} \\right)}^3}} \\right]^0}\\)<\/li>\n<li>\\({7^2} \\times {7^{ &#8211; 3}} \\times {7^{ &#8211; 1}}\\)<\/li>\n<\/ol>\n<\/td>\n<td style=\"width: 33.3333%; text-align: left;\">\n<ol style=\"list-style-type: lower-alpha;\" start=\"6\">\n<li>\\({\\left( { &#8211; 2} \\right)^3} \\times {3^3}\\)<\/li>\n<li>\\({\\left( { &#8211; 2} \\right)^3} \\times {\\left( { &#8211; 2} \\right)^5} \\div {\\left( { &#8211; 2} \\right)^{ &#8211; 3}}\\)<\/li>\n<li>\\({\\left( { &#8211; 0,5} \\right)^{ &#8211; 3}} \\times {\\left( { &#8211; 0,5} \\right)^{ &#8211; 2}}\\)<\/li>\n<li>\\({5^{ &#8211; 4}} \\div {5^3} \\times {\\left( { &#8211; \\frac{1}{5}} \\right)^{ &#8211; 7}}\\)<\/li>\n<li>\\(\\left( {2 \\times {2^4}} \\right) \\div \\left( {{2^{10}} \\times {2^{ &#8211; 3}}} \\right)\\)<\/li>\n<\/ol>\n<\/td>\n<td style=\"width: 33.3333%; text-align: left;\">\n<ol style=\"list-style-type: lower-alpha;\" start=\"11\">\n<li>\\(\\frac{5}{4} \\div {\\left( {\\frac{5}{4}} \\right)^{ &#8211; 2}}\\)<\/li>\n<li>\\({\\left( { &#8211; \\frac{1}{7}} \\right)^{ &#8211; 2}} \\times {7^{ &#8211; 2}}\\)<\/li>\n<li>\\({\\left( { &#8211; \\frac{1}{2}} \\right)^0} \\div {\\left( { &#8211; \\frac{1}{2}} \\right)^{ &#8211; 4}} \\times {\\left( { &#8211; \\frac{1}{2}} \\right)^{ &#8211; 2}}\\)<\/li>\n<li>\\({\\left( {1 + \\frac{1}{3}} \\right)^{ &#8211; 7}} \\times {\\left( {\\frac{8}{3}} \\right)^7} \\div {2^4}\\)<\/li>\n<li>\\({\\left( { &#8211; \\frac{1}{2}} \\right)^3} \\div {\\left( { &#8211; \\frac{1}{2}} \\right)^2} + {\\left( { &#8211; \\frac{3}{5}} \\right)^4} \\div {\\left( { &#8211; \\frac{3}{5}} \\right)^6}\\)<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_22330' onClick='GTTabs_show(1,22330)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_22330'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>\\({\\left( {{3^2}} \\right)^{ &#8211; 1}} = {3^{2 \\times \\left( { &#8211; 1} \\right)}} = {3^{ &#8211; 2}} = {\\left( {\\frac{1}{3}} \\right)^2} = \\frac{1}{9}\\)<br><br><\/li>\n<li>\\({\\left[ {{{\\left( {\\frac{3}{2}} \\right)}^2}} \\right]^0} = {\\left( {\\frac{3}{2}} \\right)^{2 \\times 0}} = {\\left( {\\frac{3}{2}} \\right)^0} = 1\\)<br><br><\/li>\n<li>\\({\\left[ {{{\\left( { &#8211; 5} \\right)}^2}} \\right]^{ &#8211; 2}} = {\\left( { &#8211; 5} \\right)^{ &#8211; 4}} = {\\left( { &#8211; \\frac{1}{5}} \\right)^4} = \\frac{1}{{625}}\\)<br><br><\/li>\n<li>\\({\\left[ {{{\\left( { &#8211; 0,25} \\right)}^3}} \\right]^0} = {\\left( { &#8211; 0,25} \\right)^0} = 1\\)<br><br><\/li>\n<li>\\({7^2} \\times {7^{ &#8211; 3}} \\times {7^{ &#8211; 1}} = {7^{2 + \\left( { &#8211; 3} \\right) + \\left( { &#8211; 1} \\right)}} = {7^{ &#8211; 2}} = {\\left( {\\frac{1}{7}} \\right)^2} = \\frac{1}{{49}}\\)<br><br><\/li>\n<li>\\({\\left( { &#8211; 2} \\right)^3} \\times {3^3} = {\\left( { &#8211; 2 \\times 3} \\right)^3} = {\\left( { &#8211; 6} \\right)^3} = &#8211; 216\\)<br><br><\/li>\n<li>\\({\\left( { &#8211; 2} \\right)^3} \\times {\\left( { &#8211; 2} \\right)^5} \\div {\\left( { &#8211; 2} \\right)^{ &#8211; 3}} = {\\left( { &#8211; 2} \\right)^8} \\div {\\left( { &#8211; 2} \\right)^{ &#8211; 3}} = {\\left( { &#8211; 2} \\right)^{8 &#8211; \\left( { &#8211; 3} \\right)}} = {\\left( { &#8211; 2} \\right)^{11}} = &#8211; 2 \\times {2^{10}} = &#8211; 2 \\times 1024 = &#8211; 2048\\)<br><br><\/li>\n<li>\\({\\left( { &#8211; 0,5} \\right)^{ &#8211; 3}} \\times {\\left( { &#8211; 0,5} \\right)^{ &#8211; 2}} = {\\left( { &#8211; 0,5} \\right)^{ &#8211; 3 + \\left( { &#8211; 2} \\right)}} = {\\left( { &#8211; \\frac{1}{2}} \\right)^{ &#8211; 5}} = {\\left( { &#8211; 2} \\right)^5} = &#8211; 32\\)<br><br><\/li>\n<li>\\({5^{ &#8211; 4}} \\div {5^3} \\times {\\left( { &#8211; \\frac{1}{5}} \\right)^{ &#8211; 7}} = {5^{ &#8211; 7}} \\times {\\left( { &#8211; \\frac{1}{5}} \\right)^{ &#8211; 7}} = {\\left( {5 \\times \\left( { &#8211; \\frac{1}{5}} \\right)} \\right)^{ &#8211; 7}} = {\\left( { &#8211; 1} \\right)^{ &#8211; 7}} = {\\left( { &#8211; 1} \\right)^7} = &#8211; 1\\)<br><br><\/li>\n<li>\\(\\left( {2 \\times {2^4}} \\right) \\div \\left( {{2^{10}} \\times {2^{ &#8211; 3}}} \\right) = {2^5} \\div {2^7} = {2^{ &#8211; 2}} = {\\left( {\\frac{1}{2}} \\right)^2} = \\frac{1}{4}\\)<br><br><\/li>\n<li>\\(\\frac{5}{4} \\div {\\left( {\\frac{5}{4}} \\right)^{ &#8211; 2}} = {\\left( {\\frac{5}{4}} \\right)^1} \\div {\\left( {\\frac{5}{4}} \\right)^{ &#8211; 2}} = {\\left( {\\frac{5}{4}} \\right)^{1 &#8211; \\left( { &#8211; 2} \\right)}} = {\\left( {\\frac{5}{4}} \\right)^3} = \\frac{{125}}{{64}}\\)<br><br><\/li>\n<li>\\({\\left( { &#8211; \\frac{1}{7}} \\right)^{ &#8211; 2}} \\times {7^{ &#8211; 2}} = {\\left( { &#8211; \\frac{1}{7} \\times 7} \\right)^{ &#8211; 2}} = {\\left( { &#8211; 1} \\right)^{ &#8211; 2}} = {\\left( { &#8211; 1} \\right)^2} = 1\\)<br><br><\/li>\n<li>\\({\\left( { &#8211; \\frac{1}{2}} \\right)^0} \\div {\\left( { &#8211; \\frac{1}{2}} \\right)^{ &#8211; 4}} \\times {\\left( { &#8211; \\frac{1}{2}} \\right)^{ &#8211; 2}} = {\\left( { &#8211; \\frac{1}{2}} \\right)^{0 &#8211; \\left( { &#8211; 4} \\right)}} \\times {\\left( { &#8211; \\frac{1}{2}} \\right)^{ &#8211; 2}} = {\\left( { &#8211; \\frac{1}{2}} \\right)^4} \\times {\\left( { &#8211; \\frac{1}{2}} \\right)^{ &#8211; 2}} = {\\left( { &#8211; \\frac{1}{2}} \\right)^2} = \\frac{1}{4}\\)<br><br><\/li>\n<li>\\({\\left( {1 + \\frac{1}{3}} \\right)^{ &#8211; 7}} \\times {\\left( {\\frac{8}{3}} \\right)^7} \\div {2^4} = {\\left( {\\frac{4}{3}} \\right)^{ &#8211; 7}} \\times {\\left( {\\frac{8}{3}} \\right)^7} \\div {2^4} = {\\left( {\\frac{3}{4}} \\right)^7} \\times {\\left( {\\frac{8}{3}} \\right)^7} \\div {2^4} = {\\left( {\\frac{3}{4} \\times \\frac{8}{3}} \\right)^7} \\div {2^4} = {2^7} \\div {2^4} = {2^3} = 8\\)<br><br><\/li>\n<li>\\({\\left( { &#8211; \\frac{1}{2}} \\right)^3} \\div {\\left( { &#8211; \\frac{1}{2}} \\right)^2} + {\\left( { &#8211; \\frac{3}{5}} \\right)^4} \\div {\\left( { &#8211; \\frac{3}{5}} \\right)^6} = {\\left( { &#8211; \\frac{1}{2}} \\right)^1} + {\\left( { &#8211; \\frac{3}{5}} \\right)^{ &#8211; 2}} = &#8211; \\frac{1}{2} + {\\left( { &#8211; \\frac{5}{3}} \\right)^2} = &#8211; \\frac{1}{2} + \\frac{{25}}{9} = &#8211; \\frac{9}{{18}} + \\frac{{50}}{{18}} = \\frac{{41}}{{18}}\\)<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_22330' onClick='GTTabs_show(0,22330)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Calcula o valor das express\u00f5es num\u00e9ricas utilizando, sempre que poss\u00edvel, as regras de opera\u00e7\u00f5es com pot\u00eancias: \\({\\left( {{3^2}} \\right)^{ &#8211; 1}}\\) \\({\\left[ {{{\\left( {\\frac{3}{2}} \\right)}^2}} \\right]^0}\\) \\({\\left[ {{{\\left( { &#8211; 5}&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":22340,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,664],"tags":[424,142,337],"series":[],"class_list":["post-22330","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-numeros-reais","tag-8-o-ano","tag-potencias","tag-regras-operatorias-de-potencias"],"views":282,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/10\/Mat267.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/22330","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=22330"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/22330\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/22340"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=22330"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=22330"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=22330"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=22330"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}