{"id":225992,"date":"2025-06-04T19:30:47","date_gmt":"2025-06-04T19:30:47","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=225992"},"modified":"2025-06-04T19:30:50","modified_gmt":"2025-06-04T19:30:50","slug":"which-expression-is-equivalent-to-3a%cb%86s216x27-6x3-6x9-72x3-72x9","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/04\/which-expression-is-equivalent-to-3a%cb%86s216x27-6x3-6x9-72x3-72x9\/","title":{"rendered":"Which expression is equivalent to 3\u00e2\u02c6\u0161(216x^27)? 6x^3 6x^9 72x^3 72x^9"},"content":{"rendered":"\n<p>Which expression is equivalent to 3\u00e2\u02c6\u0161(216x^27)? 6x^3 6x^9 72x^3 72x^9<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>We are given the expression: 3216&#215;2733\\sqrt[3]{216x^{27}}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Simplify the cube root<\/h3>\n\n\n\n<p>We want to simplify the <strong>cube root<\/strong> of the expression inside the radical: 216&#215;273\\sqrt[3]{216x^{27}}<\/p>\n\n\n\n<p>First, break this into two parts: 2163\u22c5x273\\sqrt[3]{216} \\cdot \\sqrt[3]{x^{27}}<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The cube root of <strong>216<\/strong> is:<\/li>\n<\/ul>\n\n\n\n<p>2163=6(since&nbsp;63=216)\\sqrt[3]{216} = 6 \\quad \\text{(since } 6^3 = 216\\text{)}<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The cube root of <strong>x\u00b2\u2077<\/strong> is:<\/li>\n<\/ul>\n\n\n\n<p>x273=x27\/3=x9\\sqrt[3]{x^{27}} = x^{27\/3} = x^9<\/p>\n\n\n\n<p>So we now have: 216&#215;273=6&#215;9\\sqrt[3]{216x^{27}} = 6x^9<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Multiply by the 3 outside the radical<\/h3>\n\n\n\n<p>Now multiply this result by the 3 that was outside the cube root: 3\u22c5(6&#215;9)=18&#215;93 \\cdot (6x^9) = 18x^9<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Check the answer choices<\/h3>\n\n\n\n<p>We are given four options:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A) 6x36x^3<\/li>\n\n\n\n<li>B) 6x96x^9<\/li>\n\n\n\n<li>C) 72x372x^3<\/li>\n\n\n\n<li>D) 72x972x^9<\/li>\n<\/ul>\n\n\n\n<p>But <strong>none of these options<\/strong> say <strong>18x\u2079<\/strong>, which is the <strong>correct simplification<\/strong>.<\/p>\n\n\n\n<p>Let\u2019s double-check the problem. The original problem might have a typo \u2014 perhaps it meant: 3\u22c58&#215;273(instead&nbsp;of&nbsp;216)?3 \\cdot \\sqrt[3]{8x^{27}} \\quad \\text{(instead of 216)?}<\/p>\n\n\n\n<p>However, based on the input exactly as you typed it: 3216&#215;273=3\u22c56&#215;9=18&#215;93\\sqrt[3]{216x^{27}} = 3 \\cdot 6x^9 = 18x^9<\/p>\n\n\n\n<p>So <strong>the correct equivalent expression is<\/strong>: 18&#215;9\\boxed{18x^9}<\/p>\n\n\n\n<p>Since <strong>18x\u2079<\/strong> is not one of the listed options, the correct answer <strong>is not among the choices<\/strong>. If this was a multiple-choice question, the options may contain a <strong>mistake<\/strong>. Please double-check the original question.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-89.jpeg\" alt=\"\" class=\"wp-image-225993\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Which expression is equivalent to 3\u00e2\u02c6\u0161(216x^27)? 6x^3 6x^9 72x^3 72x^9 The Correct Answer and Explanation is: We are given the expression: 3216&#215;2733\\sqrt[3]{216x^{27}} Step 1: Simplify the cube root We want to simplify the cube root of the expression inside the radical: 216&#215;273\\sqrt[3]{216x^{27}} First, break this into two parts: 2163\u22c5x273\\sqrt[3]{216} \\cdot \\sqrt[3]{x^{27}} 2163=6(since&nbsp;63=216)\\sqrt[3]{216} = 6 \\quad [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-225992","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225992","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=225992"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225992\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=225992"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=225992"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=225992"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}