When 1,250^3\/4 is written in simplest radical form, which value remains under the radical?
2
5
6
8<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To simplify the expression ( 1250^{3\/4} ) into its simplest radical form, we need to follow a series of steps involving exponent rules and radical simplification.<\/p>\n\n\n\n The expression is given as ( 1250^{3\/4} ). According to the rules of exponents, ( a^{m\/n} ) is the same as the ( n )-th root of ( a^m ), which can also be written as ( \\sqrt[n]{a^m} ).<\/p>\n\n\n\n Thus, we rewrite ( 1250^{3\/4} ) as:<\/p>\n\n\n\n [ This expression tells us that we first take the fourth root of 1250 and then cube the result.<\/p>\n\n\n\n Now we need to simplify ( 1250^{1\/4} ). To do this, we break 1250 into its prime factors:<\/p>\n\n\n\n [ This factorization is helpful because we can now take the fourth root of each factor separately. Specifically, the fourth root of ( 5^4 ) is ( 5 ), and the fourth root of ( 2 ) remains as ( 2^{1\/4} ).<\/p>\n\n\n\n Thus, the fourth root of 1250 is:<\/p>\n\n\n\n [ Next, we cube the result of ( 1250^{1\/4} ):<\/p>\n\n\n\n [ Simplifying further:<\/p>\n\n\n\n [ So, the expression becomes:<\/p>\n\n\n\n [ The simplified radical form of ( 1250^{3\/4} ) is:<\/p>\n\n\n\n [ In this form, ( 2^{3\/4} ) is the part of the expression that remains under the radical.<\/p>\n\n\n\n The correct value that remains under the radical is 2<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":" When 1,250^3\/4 is written in simplest radical form, which value remains under the radical?2568 The Correct Answer and Explanation is : To simplify the expression ( 1250^{3\/4} ) into its simplest radical form, we need to follow a series of steps involving exponent rules and radical simplification. Step 1: Rewrite the expression with a fractional […]<\/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-169184","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/169184","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=169184"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/169184\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=169184"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=169184"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=169184"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Rewrite the expression with a fractional exponent<\/h3>\n\n\n\n
1250^{3\/4} = \\left(1250^{1\/4}\\right)^3
]<\/p>\n\n\n\nStep 2: Simplify the fourth root of 1250<\/h3>\n\n\n\n
1250 = 2 \\times 5^4
]<\/p>\n\n\n\n
1250^{1\/4} = 5 \\times 2^{1\/4}
]<\/p>\n\n\n\nStep 3: Cube the result<\/h3>\n\n\n\n
\\left(5 \\times 2^{1\/4}\\right)^3 = 5^3 \\times \\left(2^{1\/4}\\right)^3
]<\/p>\n\n\n\n
5^3 = 125 \\quad \\text{and} \\quad \\left(2^{1\/4}\\right)^3 = 2^{3\/4}
]<\/p>\n\n\n\n
1250^{3\/4} = 125 \\times 2^{3\/4}
]<\/p>\n\n\n\nStep 4: Final simplified form<\/h3>\n\n\n\n
1250^{3\/4} = 125 \\times 2^{3\/4}
]<\/p>\n\n\n\nFinal Answer:<\/h3>\n\n\n\n