{"id":197215,"date":"2023-08-11T20:10:44","date_gmt":"2023-08-11T23:10:44","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=197215"},"modified":"2023-09-09T19:47:27","modified_gmt":"2023-09-09T22:47:27","slug":"probleminha-que-potencias","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/probleminha-que-potencias\/","title":{"rendered":".Probleminha: Que pot\u00eancias!"},"content":{"rendered":"<p class=\"g2\" ><strong><a href=\"http:\/\/clubes.obmep.org.br\/blog\/?p=199977\" rel=\"noopener\" target=\"_blank\">&#9999; <span style=\"color:#778899;font-size:14px;\">Link do problema para dispositivos da <em>Apple<\/em>.<\/span><\/a><\/strong><\/p>\n<div class=\"g1n\" style=\"line-height:25px;padding-bottom:15px\">\n<p class=\"tit\" style=\"line-height:25px;margin:10px\">Problema<br \/>\n<span style=\"font-size:12px;color:#800000\"> (Indicado a partir do 9\u00ba ano do E. F.)<\/span><\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 20px;border: 0 none\"\/>\n<p>Se<br \/>\n[tex]\\qquad 2^{2008}-2^{2007}-2^{2006}+2^{2005}=k \\cdot 2^{2005}[\/tex],<br \/>\nqual o valor de [tex]k[\/tex]?<\/p>\n<p style=\"font-size: 12px;text-align:right;line-height:1px;\">Extra\u00eddo de <strong> AHSME<\/strong>.<\/p>\n<\/div>\n<p style=\"margin:40px\">\n<div class=\"g1n\" style=\"line-height:28px;\">\n<p class=\"tit\" style=\"line-height:28px;margin:10px\">Solu\u00e7\u00e3o<\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 1px; margin-bottom: 20px;border: 0 none\"\/>\n<p>Colocando [tex]2^{2005}[\/tex] em evid\u00eancia, temos:<\/p>\n<p>[tex]\\qquad 2^{2008}-2^{2007}-2^{2006}+2^{2005}=k \\cdot 2^{2005}[\/tex]<\/p>\n<p>[tex]\\qquad 2^{2005} \\cdot (2^3-2^2-2+1)=k \\cdot 2^{2005}[\/tex]<\/p>\n<p>[tex]\\qquad 2^{2005} \\cdot 3=k \\cdot 2^{2005}.[\/tex]<\/p>\n<p>Portanto, [tex]\\fcolorbox{black}{#eee0e5}{$k=3$}\\,.[\/tex]<\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 15px;border: 0 none\"\/>\n<p class=\"g2\" >Solu\u00e7\u00e3o elaborada pelos <strong>Moderadores do Blog<\/strong>.<\/p>\n<\/div>\n<p style=\"margin:30px\">\n<div style=\"border: 1px solid #616161; padding: 8px;\">\n<p style=\"text-align: justify;\"><span style=\"font-family: verdana; color: #616161;\"> Participaram da discuss\u00e3o do problema os Clubes: <strong>Geomestres Slay;<span style=\" color: #8B8682;\"> Phidias;<span style=\" color: #616161;\"> Pot\u00eancias de Euler; <span style=\" color: #8B8682;\"> Puzzlers \u03c0rados<\/span><\/span><\/strong><\/span><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>&#9999; Link do problema para dispositivos da Apple. Problema (Indicado a partir do 9\u00ba ano do E. F.) Se [tex]\\qquad 2^{2008}-2^{2007}-2^{2006}+2^{2005}=k \\cdot 2^{2005}[\/tex], qual o valor de [tex]k[\/tex]? Extra\u00eddo de AHSME. Solu\u00e7\u00e3o Colocando [tex]2^{2005}[\/tex] em evid\u00eancia, temos: [tex]\\qquad 2^{2008}-2^{2007}-2^{2006}+2^{2005}=k \\cdot 2^{2005}[\/tex] [tex]\\qquad 2^{2005} \\cdot (2^3-2^2-2+1)=k \\cdot 2^{2005}[\/tex] [tex]\\qquad 2^{2005} \\cdot 3=k \\cdot 2^{2005}.[\/tex] Portanto, [tex]\\fcolorbox{black}{#eee0e5}{$k=3$}\\,.[\/tex] &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/clubes.obmep.org.br\/blog\/probleminha-que-potencias\/\">Continue lendo<\/a><\/p>\n","protected":false},"author":164,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-onecolumn.php","meta":{"footnotes":""},"class_list":["post-197215","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/197215","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/users\/164"}],"replies":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/comments?post=197215"}],"version-history":[{"count":8,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/197215\/revisions"}],"predecessor-version":[{"id":199979,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/197215\/revisions\/199979"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=197215"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}