Find the value of (27\/8)^-2\/3 give your answer as a fraction in its simplest form<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To solve (\\left(\\frac{27}{8}\\right)^{-\\frac{2}{3}}), we will break it down step-by-step.<\/p>\n\n\n\n The negative exponent indicates that we should take the reciprocal of the base. So:<\/p>\n\n\n\n [ Now, we need to evaluate (\\left(\\frac{27}{8}\\right)^{\\frac{2}{3}}).<\/p>\n\n\n\n The fractional exponent (\\frac{2}{3}) can be interpreted as follows:<\/p>\n\n\n\n [ This means we first take the cube root of (\\frac{27}{8}) and then square the result.<\/p>\n\n\n\n To find the cube root of a fraction, take the cube root of the numerator and the denominator separately:<\/p>\n\n\n\n So:<\/p>\n\n\n\n [ Now, we square (\\frac{3}{2}):<\/p>\n\n\n\n [ Thus:<\/p>\n\n\n\n [ Going back to our original expression, we now take the reciprocal of (\\frac{9}{4}):<\/p>\n\n\n\n [ [ We used the negative exponent rule to take the reciprocal of the base. Then, we simplified the fractional exponent by first taking the cube root of (\\frac{27}{8}), which gave (\\frac{3}{2}), and then squaring this result. Finally, we found the reciprocal of (\\frac{9}{4}) to get the final answer of (\\frac{4}{9}).<\/p>\n","protected":false},"excerpt":{"rendered":" Find the value of (27\/8)^-2\/3 give your answer as a fraction in its simplest form The Correct Answer and Explanation is : To solve (\\left(\\frac{27}{8}\\right)^{-\\frac{2}{3}}), we will break it down step-by-step. Step 1: Understanding the negative exponent The negative exponent indicates that we should take the reciprocal of the base. So: [\\left(\\frac{27}{8}\\right)^{-\\frac{2}{3}} = \\frac{1}{\\left(\\frac{27}{8}\\right)^{\\frac{2}{3}}}] Now, […]<\/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-164958","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/164958","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=164958"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/164958\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=164958"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=164958"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=164958"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Understanding the negative exponent<\/h3>\n\n\n\n
\\left(\\frac{27}{8}\\right)^{-\\frac{2}{3}} = \\frac{1}{\\left(\\frac{27}{8}\\right)^{\\frac{2}{3}}}
]<\/p>\n\n\n\nStep 2: Simplifying the fractional exponent<\/h3>\n\n\n\n
\\left(\\frac{27}{8}\\right)^{\\frac{2}{3}} = \\left(\\left(\\frac{27}{8}\\right)^{\\frac{1}{3}}\\right)^2
]<\/p>\n\n\n\nStep 3: Taking the cube root of (\\frac{27}{8})<\/h3>\n\n\n\n
\n
\\left(\\frac{27}{8}\\right)^{\\frac{1}{3}} = \\frac{3}{2}
]<\/p>\n\n\n\nStep 4: Squaring the result<\/h3>\n\n\n\n
\\left(\\frac{3}{2}\\right)^2 = \\frac{9}{4}
]<\/p>\n\n\n\n
\\left(\\frac{27}{8}\\right)^{\\frac{2}{3}} = \\frac{9}{4}
]<\/p>\n\n\n\nStep 5: Taking the reciprocal<\/h3>\n\n\n\n
\\frac{1}{\\frac{9}{4}} = \\frac{4}{9}
]<\/p>\n\n\n\nFinal Answer:<\/h3>\n\n\n\n
\\left(\\frac{27}{8}\\right)^{-\\frac{2}{3}} = \\frac{4}{9}
]<\/p>\n\n\n\nExplanation Summary:<\/h3>\n\n\n\n