Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 5 - Section 5.1 - Exponents - Exercise Set: 49

Answer

$\frac{4x^{2}z^{2}}{y^{10}}$

Work Step by Step

Based on the power of a quotient rule, we know that $(\frac{a}{c})^{n}=\frac{a^{n}}{c^{n}}$ (where $n$ is a positive integer and $a$ and $c$ are real numbers). Therefore, $(\frac{-2xz}{y^{5}})^{2}=\frac{(-2)^{2}x^{2}z^{2}}{(y^{5})^{2}}=\frac{4x^{2}z^{2}}{(y^{5})^{2}}$. Based on the power rule for exponents, we know that $(a^{m})^{n}=a^{mn}$ (where $m$ and $n$ are positive integers and $a$ is a real number). Therefore, $\frac{4x^{2}z^{2}}{(y^{5})^{2}}=\frac{4x^{2}z^{2}}{y^{5\times2}}=\frac{4x^{2}z^{2}}{y^{10}}$.
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