What expression is equivalent to 4 to the negative 3 power<\/p>\n\n\n\n
The correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n The expression (4^{-3}) is equivalent to (\\frac{1}{4^3}).<\/p>\n\n\n\n When you have an exponent that is a negative number, such as (-3), it means you are taking the reciprocal of the base (which is (4) in this case) raised to the positive version of that exponent. So, (4^{-3}) becomes:<\/p>\n\n\n\n [ Now, let’s break down the steps:<\/p>\n\n\n\n Thus, the expression (4^{-3}) simplifies to (\\frac{1}{64}).<\/p>\n\n\n\n Negative exponents indicate division rather than multiplication. By using the reciprocal (flipping the base), we avoid using negative values in the calculation. This concept is essential in algebra and higher-level mathematics, allowing us to work with inverse powers of numbers. For example, (x^{-1} = \\frac{1}{x}) demonstrates how negative exponents transform expressions into fractions.<\/p>\n\n\n\n So, the correct answer to the expression (4^{-3}) is (\\frac{1}{64}).<\/p>\n","protected":false},"excerpt":{"rendered":" What expression is equivalent to 4 to the negative 3 power The correct Answer and Explanation is: The expression (4^{-3}) is equivalent to (\\frac{1}{4^3}). Explanation: When you have an exponent that is a negative number, such as (-3), it means you are taking the reciprocal of the base (which is (4) in this case) raised […]<\/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-146699","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/146699","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=146699"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/146699\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=146699"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=146699"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=146699"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Explanation:<\/h3>\n\n\n\n
4^{-3} = \\frac{1}{4^3}
]<\/p>\n\n\n\n\n
[
a^{-n} = \\frac{1}{a^n}
]
In our case, (a = 4) and (n = 3), so we rewrite (4^{-3}) as:
[
4^{-3} = \\frac{1}{4^3}
]<\/li>\n\n\n\n
[
4^3 = 4 \\times 4 \\times 4 = 64
]<\/li>\n\n\n\n
[
\\frac{1}{4^3} = \\frac{1}{64}
]<\/li>\n<\/ol>\n\n\n\nWhy This Works:<\/h3>\n\n\n\n