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 - Page 344: 50



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, $(\frac{xy^{4}}{-3z^{3}})^{3}=\frac{x^{3}(y^{4})^{3}}{(-3)^{3}(z^{3})^{3}}=\frac{x^{3}(y^{4})^{3}}{-27(z^{3})^{3}}$. 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, $\frac{x^{3}(y^{4})^{3}}{-27(z^{3})^{3}}=\frac{x^{3}\times y^{4\times3}}{-27\times z^{3\times3}}=\frac{x^{3}y^{12}}{-27z^{9}}$.
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