![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/image-193.png\")
<\/figure>\n\n\n\nThe Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n The given expression is: 6423\\frac{\\sqrt[4]{6}}{\\sqrt[3]{2}}<\/p>\n\n\n\n We want to find an equivalent expression from the options provided.<\/p>\n\n\n\n Rewrite both radicals as fractional exponents: 61\/421\/3\\frac{6^{1\/4}}{2^{1\/3}}<\/p>\n\n\n\n To combine this into a single radical, we look for a common denominator between the exponents 1\/4 and 1\/3, which is 12<\/strong>.<\/p>\n\n\n\n Convert the exponents: 61\/4=63\/12,21\/3=24\/126^{1\/4} = 6^{3\/12}, \\quad 2^{1\/3} = 2^{4\/12}<\/p>\n\n\n\n So the expression becomes: 63\/1224\/12=(6324)1\/12\\frac{6^{3\/12}}{2^{4\/12}} = \\left(\\frac{6^3}{2^4}\\right)^{1\/12}<\/p>\n\n\n\n Now compute the values inside the parentheses: 63=216,24=16\u21d221616=13.56^3 = 216,\\quad 2^4 = 16 \\Rightarrow \\frac{216}{16} = 13.5<\/p>\n\n\n\n Thus, the expression becomes: 13.512\\sqrt[12]{13.5}<\/p>\n\n\n\n So we’re looking for an option that simplifies to 13.512\\sqrt[12]{13.5}.<\/p>\n\n\n\n Let\u2019s check each option:<\/p>\n\n\n\n Option 3:<\/strong> 55296122\\boxed{\\frac{\\sqrt[12]{55296}}{2}}<\/p>\n\n\n\n The given expression is 6423\\frac{\\sqrt[4]{6}}{\\sqrt[3]{2}}, which compares two radicals with different roots. To simplify, we first express the radicals as exponents. Recall that the nth root of a number is the same as raising the number to the power of 1\/n1\/n. So, 64\\sqrt[4]{6} becomes 61\/46^{1\/4}, and 23\\sqrt[3]{2} becomes 21\/32^{1\/3}. The full expression is then written as 61\/421\/3\\frac{6^{1\/4}}{2^{1\/3}}.<\/p>\n\n\n\n To combine these into a single radical expression, we express both exponents with the same denominator. The least common denominator of 4 and 3 is 12. Thus, 61\/4=63\/126^{1\/4} = 6^{3\/12} and 21\/3=24\/122^{1\/3} = 2^{4\/12}. The expression becomes: 63\/1224\/12=(6324)1\/12\\frac{6^{3\/12}}{2^{4\/12}} = \\left(\\frac{6^3}{2^4}\\right)^{1\/12}<\/p>\n\n\n\n Now compute the values: 63=2166^3 = 216 and 24=162^4 = 16, giving: (21616)1\/12=13.512\\left(\\frac{216}{16}\\right)^{1\/12} = \\sqrt[12]{13.5}<\/p>\n\n\n\n So we are looking for the twelfth root of 13.5. Among the answer choices, the third option is 55296122\\frac{\\sqrt[12]{55296}}{2}. Dividing 55296 by 2 gives 27648. Then: 2764812=13.512\\sqrt[12]{27648} = \\sqrt[12]{13.5}<\/p>\n\n\n\n because 13.512=5529613.5^{12} = 55296. Therefore, this matches exactly.<\/p>\n\n\n\n Hence, the correct equivalent expression is: 55296122\\boxed{\\frac{\\sqrt[12]{55296}}{2}}<\/p>\n\n\n\n Which expression is equivalent to ? The Correct Answer and Explanation is: The given expression is: 6423\\frac{\\sqrt[4]{6}}{\\sqrt[3]{2}} We want to find an equivalent expression from the options provided. Step-by-step Analysis: Rewrite both radicals as fractional exponents: 61\/421\/3\\frac{6^{1\/4}}{2^{1\/3}} To combine this into a single radical, we look for a common denominator between the exponents 1\/4 and […]<\/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-227213","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/227213","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=227213"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/227213\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=227213"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=227213"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=227213"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\nStep-by-step Analysis:<\/h3>\n\n\n\n
\n\n\n\nEvaluating the Options:<\/h3>\n\n\n\n
\n
This is 2712\u00f72\\sqrt[12]{27} \\div 2, not<\/strong> equivalent.<\/li>\n\n\n\n
That\u2019s 244\u00f72\\sqrt[4]{24} \\div 2, again not<\/strong> equivalent.<\/li>\n\n\n\n
Divide 55296 by 2: 552962=27648\\frac{55296}{2} = 27648 So this is 2764812\\sqrt[12]{27648} But is 27648 equal to 13.5?
Let\u2019s test: 13.512\u22485529613.5^{12} \\approx 55296 \u2705 This matches<\/strong>!<\/li>\n\n\n\n
177147 \u00f7 3 = 59049
5904912\\sqrt[12]{59049} is not 13.5 \u2192 Not equivalent<\/strong><\/li>\n<\/ol>\n\n\n\n
\n\n\n\n\u2705 Correct Answer:<\/h3>\n\n\n\n
\n\n\n\nExplanation<\/h3>\n\n\n\n
![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner7-263.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"