Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 7 - Exponents and Exponential Functions - 7-4 More Multiplication Properties of Exponents - Practice and Problem-Solving Exercises - Page 437: 53



Work Step by Step

Given : $(5x^{y})^{2}$ = $25x^{-4}$ (The empty square box is represented as y) This implies : $5^{2}x^{2y}$ = $25x^{-4}$ (since $(ab)^{n}=a^{n}b^{n}$ and $(a^{m})^{n}=a^{mn}$) Thus, $25$ X $x^{2y}$ = $25$ X $x^{-4}$ (since $5^{2} = 25$) Hence, $x^{2y}=x^{-4}$ This implies : $2y=-4$ Hence, $y=\frac{-4}{2}=-2$ Final result : The value in the blank is $-2$
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