Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 7 - Exponents and Exponential Functions - 7-4 Division Properties of Exponents - Practice and Problem-Solving Exercises - Page 444: 71



Work Step by Step

You are given ($\frac{3xy^5}{x^4y}$$)^{-2}$.Simplify the expression: ($\frac{x^4y}{3xy^5}$$)^{2}$ -Use the exponent rule that $x^{-y}$=$\frac{1}{x^y}$- ($\frac{x^4{^-}{^1}y^1{^-}{^5}}{3}$$)^{2}$ -subtract the exponents since you are dividing powers with the same base- ($\frac{x^3y{^-}{^4}}{3}$$)^{2}$ -simplify the expression- ($\frac{x^3}{3y^4}$$)^{2}$ -Use the exponent rule that $x^{-y}$=$\frac{1}{x^y}$- $\frac{x^6}{9y^8}$ -raise the numerator and denominator to the power 2- The simplified expression is $\frac{x^6}{9y^8}$
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