{"id":146395,"date":"2024-09-30T19:44:15","date_gmt":"2024-09-30T19:44:15","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=146395"},"modified":"2024-09-30T19:44:17","modified_gmt":"2024-09-30T19:44:17","slug":"which-is-equivalent-tostartroot-10-endroot-superscript-three-fourths-x","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/09\/30\/which-is-equivalent-tostartroot-10-endroot-superscript-three-fourths-x\/","title":{"rendered":"Which is equivalent toStartRoot 10 EndRoot Superscript three-fourths x"},"content":{"rendered":"\n<p>Which is equivalent toStartRoot 10 EndRoot Superscript three-fourths x ?<br>RootIndex 3 StartRoot 10 EndRoot Superscript 4 x<br>RootIndex 4 StartRoot 10 EndRoot Superscript 3 x<br>RootIndex 5 StartRoot 10 EndRoot Superscript 4 x<br>RootIndex 8 StartRoot 10 EndRoot Superscript 3 x<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To determine which expression is equivalent to ( \\sqrt[4]{10^{\\frac{3}{4}} x} ), we can use properties of exponents and roots.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step-by-Step Breakdown<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Understanding the Expression<\/strong>:<br>The expression ( \\sqrt[4]{10^{\\frac{3}{4}} x} ) can be rewritten using exponent notation:<br>[<br>\\sqrt[4]{10^{\\frac{3}{4}} x} = (10^{\\frac{3}{4}} x)^{\\frac{1}{4}} = 10^{\\frac{3}{4} \\cdot \\frac{1}{4}} x^{\\frac{1}{4}} = 10^{\\frac{3}{16}} x^{\\frac{1}{4}}.<br>]<\/li>\n\n\n\n<li><strong>Simplifying the Terms<\/strong>:<br>From the simplification above, we see that:<br>[<br>\\sqrt[4]{10^{\\frac{3}{4}} x} = 10^{\\frac{3}{16}} \\cdot x^{\\frac{1}{4}}.<br>]<\/li>\n\n\n\n<li><strong>Comparing with Given Options<\/strong>:<br>Now, let\u2019s analyze the provided options:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Option 1<\/strong>: ( \\sqrt[3]{10^{4} x} )<br>[<br>= (10^4 x)^{\\frac{1}{3}} = 10^{\\frac{4}{3}} x^{\\frac{1}{3}}.<br>]<\/li>\n\n\n\n<li><strong>Option 2<\/strong>: ( \\sqrt[4]{10^{3} x} )<br>[<br>= (10^3 x)^{\\frac{1}{4}} = 10^{\\frac{3}{4}} x^{\\frac{1}{4}}.<br>]<\/li>\n\n\n\n<li><strong>Option 3<\/strong>: ( \\sqrt[5]{10^{4} x} )<br>[<br>= (10^4 x)^{\\frac{1}{5}} = 10^{\\frac{4}{5}} x^{\\frac{1}{5}}.<br>]<\/li>\n\n\n\n<li><strong>Option 4<\/strong>: ( \\sqrt[8]{10^{3} x} )<br>[<br>= (10^3 x)^{\\frac{1}{8}} = 10^{\\frac{3}{8}} x^{\\frac{1}{8}}.<br>]<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Finding the Equivalent Expression<\/strong>:<br>To find an equivalent expression to ( 10^{\\frac{3}{16}} x^{\\frac{1}{4}} ), we observe the exponents of 10 and ( x ) in the simplified expressions:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>None of the options have the exponent ( \\frac{3}{16} ) for 10 or ( \\frac{1}{4} ) for ( x ).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>After evaluating all options, we conclude that none of the provided options are equivalent to ( \\sqrt[4]{10^{\\frac{3}{4}} x} ).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Correct Expression<\/h3>\n\n\n\n<p>The equivalent expression in this context can be represented as ( 10^{\\frac{3}{16}} x^{\\frac{1}{4}} ), which is not listed among the options. Therefore, it is crucial to ensure the context or values are correctly interpreted or restated to find an appropriate match.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Which is equivalent toStartRoot 10 EndRoot Superscript three-fourths x ?RootIndex 3 StartRoot 10 EndRoot Superscript 4 xRootIndex 4 StartRoot 10 EndRoot Superscript 3 xRootIndex 5 StartRoot 10 EndRoot Superscript 4 xRootIndex 8 StartRoot 10 EndRoot Superscript 3 x The Correct Answer and Explanation is : To determine which expression is equivalent to ( \\sqrt[4]{10^{\\frac{3}{4}} x} [&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-146395","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/146395","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=146395"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/146395\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=146395"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=146395"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=146395"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}