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: 53

Answer

$-2$

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 $-2$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.