{"id":19050,"date":"2025-06-13T12:26:11","date_gmt":"2025-06-13T12:26:11","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=19050"},"modified":"2025-06-13T12:26:17","modified_gmt":"2025-06-13T12:26:17","slug":"which-expression-is-equivalent-to-the-cube-root-of-216x27","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/which-expression-is-equivalent-to-the-cube-root-of-216x27\/","title":{"rendered":"Which expression is equivalent to the cube root of 216x^27"},"content":{"rendered":"\n<p>Which expression is equivalent to the cube root of 216x^27?<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Correct Answer:<\/h3>\n\n\n\n<p>The expression equivalent to the cube root of 216x27216x^{27} is: 216&#215;273=6&#215;9\\sqrt[3]{216x^{27}} = 6x^9<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation (Approximately 300 Words):<\/h3>\n\n\n\n<p>To simplify the cube root of an expression like 216&#215;273\\sqrt[3]{216x^{27}}, we apply the <strong>properties of radicals and exponents<\/strong>.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Step 1: Factor the expression inside the radical<\/h4>\n\n\n\n<p>Start with: 216&#215;273\\sqrt[3]{216x^{27}}<\/p>\n\n\n\n<p>We break this down into two parts: the cube root of the number and the cube root of the variable part: 2163\u22c5x273\\sqrt[3]{216} \\cdot \\sqrt[3]{x^{27}}<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Step 2: Simplify the cube root of the number<\/h4>\n\n\n\n<p>216216 is a <strong>perfect cube<\/strong>. We can find this by testing small integers: 63=6\u22c56\u22c56=2166^3 = 6 \\cdot 6 \\cdot 6 = 216<\/p>\n\n\n\n<p>So: 2163=6\\sqrt[3]{216} = 6<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Step 3: Simplify the cube root of the variable expression<\/h4>\n\n\n\n<p>Use the <strong>rule of exponents under radicals<\/strong>: x273=x27\u00f73=x9\\sqrt[3]{x^{27}} = x^{27 \\div 3} = x^9<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Step 4: Multiply the simplified parts<\/h4>\n\n\n\n<p>Now that both parts are simplified: 216&#215;273=6\u22c5x9=6&#215;9\\sqrt[3]{216x^{27}} = 6 \\cdot x^9 = 6x^9<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Key Concepts Used:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Cube root<\/strong> of a product: ab3=a3\u22c5b3\\sqrt[3]{ab} = \\sqrt[3]{a} \\cdot \\sqrt[3]{b}<\/li>\n\n\n\n<li><strong>Cube root of a power<\/strong>: xn3=xn\/3\\sqrt[3]{x^n} = x^{n\/3}, provided nn is divisible by 3<\/li>\n\n\n\n<li>Recognizing perfect cubes: 13=1,23=8,33=27,43=64,53=125,63=2161^3 = 1, 2^3 = 8, 3^3 = 27, 4^3 = 64, 5^3 = 125, 6^3 = 216<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>6&#215;9\\boxed{6x^9}<\/p>\n\n\n\n<p>This simplified expression is much easier to work with in algebra and calculus and represents the exact same value as the original radical expression.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Which expression is equivalent to the cube root of 216x^27? The correct answer and explanation is: Correct Answer: The expression equivalent to the cube root of 216x27216x^{27} is: 216&#215;273=6&#215;9\\sqrt[3]{216x^{27}} = 6x^9 Explanation (Approximately 300 Words): To simplify the cube root of an expression like 216&#215;273\\sqrt[3]{216x^{27}}, we apply the properties of radicals and exponents. Step 1: [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-19050","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/19050","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=19050"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/19050\/revisions"}],"predecessor-version":[{"id":19051,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/19050\/revisions\/19051"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=19050"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=19050"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=19050"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}