Which is equivalent to RootIndex 3 StartRoot 8 EndRoot Superscript x? RootIndex x StartRoot 8 EndRoot Superscript x 8 Superscript StartFraction 3 Over x EndFraction 8 Superscript StartFraction x Over 3 EndFraction 8 Superscript 3 x<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n The given expression is:<\/p>\n\n\n\n [ We need to simplify this and express it in a form that matches one of the provided options.<\/p>\n\n\n\n The cube root of ( 8^x ) can be rewritten using exponent rules:<\/p>\n\n\n\n [ By the power of a power rule ( (a^m)^n = a^{m \\cdot n} ), we can multiply the exponents:<\/p>\n\n\n\n [ Now, we know that ( 8 = 2^3 ), so we can substitute this into the expression:<\/p>\n\n\n\n [ Using the power of a power rule again, ( (a^m)^n = a^{m \\cdot n} ), we get:<\/p>\n\n\n\n [ Thus, the expression ( \\sqrt[3]{8^x} ) simplifies to ( 2^x ).<\/p>\n\n\n\n Among the options:<\/p>\n\n\n\n We can see that the expression ( 8^{\\frac{x}{3}} ) directly matches the simplified form of the original expression.<\/p>\n\n\n\n Thus, the correct answer is:<\/p>\n\n\n\n [ The cube root of ( 8^x ), or ( \\sqrt[3]{8^x} ), was simplified using the properties of exponents. The cube root is the same as raising the expression to the ( \\frac{1}{3} ) power. We then applied the rule that ( (a^m)^n = a^{m \\cdot n} ) to simplify the expression. By substituting ( 8 = 2^3 ), we eventually arrived at the final simplified form of ( 8^{\\frac{x}{3}} ), which matches one of the given options.<\/p>\n","protected":false},"excerpt":{"rendered":" Which is equivalent to RootIndex 3 StartRoot 8 EndRoot Superscript x? RootIndex x StartRoot 8 EndRoot Superscript x 8 Superscript StartFraction 3 Over x EndFraction 8 Superscript StartFraction x Over 3 EndFraction 8 Superscript 3 x The Correct Answer and Explanation is: The given expression is: [\\sqrt[3]{8^x}] We need to simplify this and express it […]<\/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-168145","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168145","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=168145"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168145\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=168145"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=168145"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=168145"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\\sqrt[3]{8^x}
]<\/p>\n\n\n\nStep 1: Rewriting the expression<\/h3>\n\n\n\n
\\sqrt[3]{8^x} = (8^x)^{\\frac{1}{3}}
]<\/p>\n\n\n\n
(8^x)^{\\frac{1}{3}} = 8^{\\frac{x}{3}}
]<\/p>\n\n\n\nStep 2: Expressing ( 8^{\\frac{x}{3}} )<\/h3>\n\n\n\n
8^{\\frac{x}{3}} = (2^3)^{\\frac{x}{3}}
]<\/p>\n\n\n\n
(2^3)^{\\frac{x}{3}} = 2^{3 \\cdot \\frac{x}{3}} = 2^x
]<\/p>\n\n\n\nStep 3: Matching the answer<\/h3>\n\n\n\n
\n
8^{\\frac{x}{3}}
]<\/p>\n\n\n\nExplanation:<\/h3>\n\n\n\n