3\/2 to the power of 3 as a fraction<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The correct answer is: frac{27}{8}<\/strong><\/mark><\/p>\n\n\n\n To calculate ( \\left(\\frac{3}{2}\\right)^3 ), we raise both the numerator and the denominator to the power of 3.<\/p>\n\n\n\n Putting it all together, we get: Explanation<\/strong>:<\/p>\n\n\n\n When we deal with fractions and exponents, it’s essential to remember the basic rules of exponents. For any fraction ( \\frac{a}{b} ) raised to the power of ( n ), the result can be expressed as:<\/p>\n\n\n\n [ This means you raise both the numerator and denominator to the same exponent. In this case, ( a = 3 ), ( b = 2 ), and ( n = 3 ).<\/p>\n\n\n\n Raising the numerator and the denominator separately simplifies the calculation and helps to maintain accuracy.<\/p>\n\n\n\n Converting to Mixed Numbers<\/strong>:<\/p>\n\n\n\n The fraction ( \\frac{27}{8} ) can also be converted into a mixed number. To do this, we divide 27 by 8.<\/p>\n\n\n\n [ Thus, ( \\frac{27}{8} ) can be expressed as:<\/p>\n\n\n\n [ Final Result<\/strong>:<\/p>\n\n\n\n So, the final answer to ( \\left(\\frac{3}{2}\\right)^3 ) is ( \\frac{27}{8} ), which can also be represented as the mixed number ( 3 \\frac{3}{8} ). This demonstrates how exponentiation works with fractions and provides an understanding of how to manipulate and convert between improper fractions and mixed numbers.<\/p>\n","protected":false},"excerpt":{"rendered":" 3\/2 to the power of 3 as a fraction The Correct Answer and Explanation is : The correct answer is: frac{27}{8} To calculate ( \\left(\\frac{3}{2}\\right)^3 ), we raise both the numerator and the denominator to the power of 3. Putting it all together, we get:[\\left(\\frac{3}{2}\\right)^3 = \\frac{27}{8}] Explanation: When we deal with fractions and exponents, […]<\/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-156914","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/156914","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=156914"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/156914\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=156914"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=156914"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=156914"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
[
3^3 = 3 \\times 3 \\times 3 = 27
]<\/li>\n\n\n\n
[
2^3 = 2 \\times 2 \\times 2 = 8
]<\/li>\n<\/ol>\n\n\n\n
[
\\left(\\frac{3}{2}\\right)^3 = \\frac{27}{8}
]<\/p>\n\n\n\n
\\left(\\frac{a}{b}\\right)^n = \\frac{a^n}{b^n}
]<\/p>\n\n\n\n
27 \\div 8 = 3 \\quad \\text{(with a remainder of 3)}
]<\/p>\n\n\n\n
3 \\frac{3}{8}
]<\/p>\n\n\n\n