The given expression is: 205\u22c52\u22123\\frac{20}{5 \\cdot 2^{-3}}5\u22c52\u2212320\u200b<\/p>\n\n\n\n
Step 1: Simplify the exponent<\/h3>\n\n\n\n
First, recall that 2\u221232^{-3}2\u22123 means: 2\u22123=123=182^{-3} = \\frac{1}{2^3} = \\frac{1}{8}2\u22123=231\u200b=81\u200b<\/p>\n\n\n\n
Now, substitute this value into the original expression: 205\u22c518\\frac{20}{5 \\cdot \\frac{1}{8}}5\u22c581\u200b20\u200b<\/p>\n\n\n\n
Step 2: Simplify the denominator<\/h3>\n\n\n\n
Next, simplify the denominator. When you multiply 5 by 18\\frac{1}{8}81\u200b, you get: 5\u22c518=585 \\cdot \\frac{1}{8} = \\frac{5}{8}5\u22c581\u200b=85\u200b<\/p>\n\n\n\n
So, the expression becomes: 2058\\frac{20}{\\frac{5}{8}}85\u200b20\u200b<\/p>\n\n\n\n
Step 3: Divide by a fraction<\/h3>\n\n\n\n
To divide by a fraction, you multiply by the reciprocal of the fraction. The reciprocal of 58\\frac{5}{8}85\u200b is 85\\frac{8}{5}58\u200b. So the expression becomes: 20\u22c58520 \\cdot \\frac{8}{5}20\u22c558\u200b<\/p>\n\n\n\n
Step 4: Simplify the multiplication<\/h3>\n\n\n\n
Now, multiply the numerator and denominator: 20\u22c585=20\u22c585=160520 \\cdot \\frac{8}{5} = \\frac{20 \\cdot 8}{5} = \\frac{160}{5}20\u22c558\u200b=520\u22c58\u200b=5160\u200b<\/p>\n\n\n\n
Now simplify: 1605=32\\frac{160}{5} = 325160\u200b=32<\/p>\n\n\n\n
Final Answer:<\/h3>\n\n\n\n
The value of the expression is 323232.<\/p>\n\n\n\n
This step-by-step simplification shows how to handle negative exponents, multiplication, and division of fractions to reach the correct result.<\/p>\n\n\n\n Evaluate: \\frac{20}{5 \\cdot 2^{-3}} The Correct Answer and Explanation is: The given expression is: 205\u22c52\u22123\\frac{20}{5 \\cdot 2^{-3}}5\u22c52\u2212320\u200b Step 1: Simplify the exponent First, recall that 2\u221232^{-3}2\u22123 means: 2\u22123=123=182^{-3} = \\frac{1}{2^3} = \\frac{1}{8}2\u22123=231\u200b=81\u200b Now, substitute this value into the original expression: 205\u22c518\\frac{20}{5 \\cdot \\frac{1}{8}}5\u22c581\u200b20\u200b Step 2: Simplify the denominator Next, simplify the denominator. When you multiply […]<\/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-258182","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/258182","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=258182"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/258182\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=258182"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=258182"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=258182"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-891.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"