Evaluate. Write your answer as a fraction in simplest form ((4)\/(5))^(3) <\/p>\n\n\n\n
(A) 4\/5 (B) 5\/4 (C) 64\/125 (D) 125\/64<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n The problem asks to evaluate (\\left( \\frac{4}{5} \\right)^3) and express the result as a fraction in its simplest form.<\/p>\n\n\n\n The expression (\\left( \\frac{4}{5} \\right)^3) means that we are raising the fraction (\\frac{4}{5}) to the power of 3. This involves multiplying the fraction by itself three times: To multiply fractions, multiply the numerators together and multiply the denominators together: The fraction (\\frac{64}{125}) is already in its simplest form because 64 and 125 have no common factors other than 1. 64 is a power of 2 ((2^6)) and 125 is a power of 5 ((5^3)), so they have no common prime factors.<\/p>\n\n\n\n Now, let’s look at the answer choices:<\/p>\n\n\n\n Since we calculated that (\\left( \\frac{4}{5} \\right)^3 = \\frac{64}{125}), the correct answer is (C) (\\frac{64}{125})<\/strong>.<\/p>\n\n\n\n The correct answer is (C) (\\frac{64}{125})<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":" Evaluate. Write your answer as a fraction in simplest form ((4)\/(5))^(3) (A) 4\/5 (B) 5\/4 (C) 64\/125 (D) 125\/64 The Correct Answer and Explanation is: The problem asks to evaluate (\\left( \\frac{4}{5} \\right)^3) and express the result as a fraction in its simplest form. Step 1: Understanding the problem The expression (\\left( \\frac{4}{5} \\right)^3) means […]<\/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-167545","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167545","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=167545"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167545\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=167545"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=167545"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=167545"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Understanding the problem<\/h3>\n\n\n\n
[
\\left( \\frac{4}{5} \\right)^3 = \\frac{4}{5} \\times \\frac{4}{5} \\times \\frac{4}{5}
]<\/p>\n\n\n\nStep 2: Multiply the fractions<\/h3>\n\n\n\n
[
\\text{Numerator: } 4 \\times 4 \\times 4 = 64
]
[
\\text{Denominator: } 5 \\times 5 \\times 5 = 125
]
Thus, the result of multiplying the fractions is:
[
\\frac{64}{125}
]<\/p>\n\n\n\nStep 3: Simplifying the result<\/h3>\n\n\n\n
Step 4: Answer choices<\/h3>\n\n\n\n
\n
Conclusion<\/h3>\n\n\n\n