Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 5 - Section 5.2 - More Work with Exponents and Scientific Notation - Exercise Set: 11



Work Step by Step

We are given the expression $(\frac{x^{7}y^{-3}}{z^{-4}})^{-5}$. To simplify, we can use the power of a quotient rule, which holds that $(\frac{a}{b})^{n}=\frac{a^{n}}{b^{n}}$, $b\ne0$ (where a and b are real numbers, and n is an integer). $(\frac{x^{7}y^{-3}}{z^{-4}})^{-5}=\frac{(x^{7}y^{-3})^{-5}}{(z^{-4})^{-5}}$ To simplify further, we can use the power rule, which holds that $(a^{m})^{n}=a^{m\times n}$ (where a is a real number, and m and n are integers). $\frac{(x^{7}y^{-3})^{-5}}{(z^{-4})^{-5}}=\frac{(x^{7\times-5})\times(y^{-3\times-5})}{z^{-4\times-5}}=\frac{x^{-35}y^{15}}{z^{20}}=\frac{y^{15}}{x^{35}z^{20}}$
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