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: 103

Answer

$\frac{x^{18}}{4y^{22}}$

Work Step by Step

Based on the power of a product rule, we know that $(ab)^{n}=a^{n}b^{n}$ (where $n$ is a positive integer and $a$ and $b$ are real numbers). Therefore, $(\frac{5x^{9}}{10y^{11}})^{2}=\frac{5^{2}(x^{9})^{2}}{10^{2}(y^{11})^{2}}=\frac{25(x^{9})^{2}}{100(y^{11})^{2}}=\frac{(x^{9})^{2}}{4(y^{11})^{2}}$. 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, $\frac{(x^{9})^{2}}{4(y^{11})^{2}}=\frac{x^{9\times2}}{4y^{11\times2}}=\frac{x^{18}}{4y^{22}}$.
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