{"id":267721,"date":"2025-07-23T16:30:18","date_gmt":"2025-07-23T16:30:18","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=267721"},"modified":"2025-07-23T16:30:20","modified_gmt":"2025-07-23T16:30:20","slug":"what-is-the-correct-expanded-form-and-value-of-leftfrac45right3-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/23\/what-is-the-correct-expanded-form-and-value-of-leftfrac45right3-2\/","title":{"rendered":"What is the correct expanded form and value of \\left(\\frac{4}{5}\\right)^3"},"content":{"rendered":"\n

What is the correct expanded form and value of \\left(\\frac{4}{5}\\right)^3? \\ ? \\frac{4}{5} + \\frac{4}{5} + \\frac{4}{5} = \\frac{12}{5} \\ ? \\frac{4}{5} \\cdot \\frac{4}{5} \\cdot \\frac{4}{5} = \\frac{64}{125} \\ ? \\frac{4 + 4 + 4}{5} = \\frac{12}{5} \\ ? \\frac{5}{4} \\cdot \\frac{5}{4} \\cdot \\frac{5}{4} = \\frac{125}{64}<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/strong><\/p>\n\n\n\n

The expression (45)3\\left( \\frac{4}{5} \\right)^3(54\u200b)3 represents the cube of the fraction 45\\frac{4}{5}54\u200b. Let’s break down the components of this operation and clarify the confusion with the options.<\/p>\n\n\n\n

Step 1: Understanding the operation<\/h3>\n\n\n\n

When we cube a fraction, we multiply the fraction by itself three times. This gives:(45)3=45\u22c545\u22c545\\left( \\frac{4}{5} \\right)^3 = \\frac{4}{5} \\cdot \\frac{4}{5} \\cdot \\frac{4}{5}(54\u200b)3=54\u200b\u22c554\u200b\u22c554\u200b<\/p>\n\n\n\n

Step 2: Multiplying the fractions<\/h3>\n\n\n\n

To multiply fractions, multiply the numerators and denominators separately:45\u22c545=4\u22c545\u22c55=1625\\frac{4}{5} \\cdot \\frac{4}{5} = \\frac{4 \\cdot 4}{5 \\cdot 5} = \\frac{16}{25}54\u200b\u22c554\u200b=5\u22c554\u22c54\u200b=2516\u200b<\/p>\n\n\n\n

Now, multiply this result by the third 45\\frac{4}{5}54\u200b:1625\u22c545=16\u22c5425\u22c55=64125\\frac{16}{25} \\cdot \\frac{4}{5} = \\frac{16 \\cdot 4}{25 \\cdot 5} = \\frac{64}{125}2516\u200b\u22c554\u200b=25\u22c5516\u22c54\u200b=12564\u200b<\/p>\n\n\n\n

Thus, the correct value of (45)3\\left( \\frac{4}{5} \\right)^3(54\u200b)3 is 64125\\frac{64}{125}12564\u200b.<\/p>\n\n\n\n

Step 3: Explanation of the incorrect options<\/h3>\n\n\n\n
    \n
  • Option 1<\/strong>: 45+45+45=125\\frac{4}{5} + \\frac{4}{5} + \\frac{4}{5} = \\frac{12}{5}54\u200b+54\u200b+54\u200b=512\u200b
    This is a sum, not a product. When you add 45\\frac{4}{5}54\u200b three times, you get 125\\frac{12}{5}512\u200b, but this is not the correct operation for cubing the fraction.<\/li>\n\n\n\n
  • Option 2<\/strong>: 45\u22c545\u22c545=64125\\frac{4}{5} \\cdot \\frac{4}{5} \\cdot \\frac{4}{5} = \\frac{64}{125}54\u200b\u22c554\u200b\u22c554\u200b=12564\u200b
    This is the correct result and matches the correct calculation we did above.<\/li>\n\n\n\n
  • Option 3<\/strong>: 4+4+45=125\\frac{4 + 4 + 4}{5} = \\frac{12}{5}54+4+4\u200b=512\u200b
    This is again a sum in the numerator, not a product of fractions. It doesn\u2019t correctly represent cubing the fraction.<\/li>\n\n\n\n
  • Option 4<\/strong>: 54\u22c554\u22c554=12564\\frac{5}{4} \\cdot \\frac{5}{4} \\cdot \\frac{5}{4} = \\frac{125}{64}45\u200b\u22c545\u200b\u22c545\u200b=64125\u200b
    This operation involves cubing 54\\frac{5}{4}45\u200b, which is a different fraction than 45\\frac{4}{5}54\u200b, so it’s irrelevant to the original problem.<\/li>\n<\/ul>\n\n\n\n

    Final Answer:<\/h3>\n\n\n\n

    The correct expanded form and value of (45)3\\left( \\frac{4}{5} \\right)^3(54\u200b)3 is:64125\\frac{64}{125}12564\u200b<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    What is the correct expanded form and value of \\left(\\frac{4}{5}\\right)^3? \\ ? \\frac{4}{5} + \\frac{4}{5} + \\frac{4}{5} = \\frac{12}{5} \\ ? \\frac{4}{5} \\cdot \\frac{4}{5} \\cdot \\frac{4}{5} = \\frac{64}{125} \\ ? \\frac{4 + 4 + 4}{5} = \\frac{12}{5} \\ ? \\frac{5}{4} \\cdot \\frac{5}{4} \\cdot \\frac{5}{4} = \\frac{125}{64} The Correct Answer and Explanation is: The expression (45)3\\left( […]<\/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-267721","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/267721","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=267721"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/267721\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=267721"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=267721"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=267721"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}