Which is equivalent to sqrt(10) * 3\/4 * ? X (root(10, 3)) ^ (4x) (root(10, 4)) ^ (3x) (root(10, 6)) ^ (4x) (root(10, 8)) ^ (3x)<\/p>\n\n\n\n
The Correct answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The correct answer is: {1}{10}}<\/strong><\/mark><\/p>\n\n\n\n To find an expression equivalent to (\\sqrt{10} \\cdot \\frac{3}{4} \\cdot ?) in terms of the given roots of 10, we first need to understand the terms involved.<\/p>\n\n\n\n We are provided with the expression: Let\u2019s express the given terms with exponents:<\/p>\n\n\n\n Now, we can express the equation as: To find the equivalent expression, we need to analyze each of the given roots and their exponents:<\/p>\n\n\n\n To find (?), we need (1\/2 + k) to equal one of the exponents from the roots. This leads us to: Therefore, the correct value of (?) that makes the expression equivalent is: Which is equivalent to sqrt(10) * 3\/4 * ? X (root(10, 3)) ^ (4x) (root(10, 4)) ^ (3x) (root(10, 6)) ^ (4x) (root(10, 8)) ^ (3x) The Correct answer and Explanation is : The correct answer is: {1}{10}} To find an expression equivalent to (\\sqrt{10} \\cdot \\frac{3}{4} \\cdot ?) in terms of the given roots […]<\/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-149888","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/149888","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=149888"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/149888\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=149888"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=149888"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=149888"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Definitions:<\/h3>\n\n\n\n
\n
\n
\n
\n
Given Expression:<\/h3>\n\n\n\n
[
\\sqrt{10} \\cdot \\frac{3}{4} \\cdot ?
]
We want to find (?) such that:
[
\\sqrt{10} \\cdot \\frac{3}{4} \\cdot ? = \\text{some combination of the roots}
]<\/p>\n\n\n\nEquating Powers of 10:<\/h3>\n\n\n\n
\n
[
10^{1\/2} \\cdot \\frac{3}{4} \\cdot 10^k = 10^{1\/2 + k} \\cdot \\frac{3}{4}
]<\/p>\n\n\n\n\n
Finding the Right Expression:<\/h3>\n\n\n\n
[
\\frac{3}{4} + k = 0 \\implies k = -\\frac{1}{4}
]
Thus,
[
? = 10^{-1\/4} = \\sqrt[4]{\\frac{1}{10}}
]<\/p>\n\n\n\nConclusion:<\/h3>\n\n\n\n
[
\\sqrt[4]{\\frac{1}{10}}.
]
This approach demonstrates how to manipulate the exponents and roots of 10 to find an equivalent expression, emphasizing the importance of understanding properties of exponents in algebra.<\/p>\n","protected":false},"excerpt":{"rendered":"