Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 1 - Section 1.6 - Properties of Integral Exponents - Exercise Set - Page 80: 113



Work Step by Step

$$(\frac{x^{-5}y^{8}}{3})^{-4}$$ Recall the power rule: $(a^{m})^{n}=a^{mn}$ Thus, $=\frac{x^{-5\cdot-4}y^{8\cdot-4}}{3^{-4}}$ $=\frac{x^{20}y^{-32}}{3^{-4}}$ Recall the negative exponent rule: $a^{−n}=\frac{1}{a^{n}}$ and $\frac{1}{a^{-n}} = a^{n}$ Thus, $=\frac{x^{20}y^{-32}}{3^{-4}}$ $=\frac{x^{20}3^{4}}{y^{32}}$ $=\frac{81x^{20}}{y^{32}}$
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