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: 7

Answer

$16x^{20}y^{12}$

Work Step by Step

We are given the expression $(\frac{2x^{5}}{y^{-3}})^{4}$. We can use the power of a quotient rule to simplify, 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). $(\frac{2x^{5}}{y^{-3}})^{4}=\frac{(2x^{5})^{4}}{(y^{-3})^{4}}$ 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). $\frac{(2x^{5})^{4}}{(y^{-3})^{4}}=\frac{2^{4}x^{5\times4}}{y^{-3\times4}}=\frac{16x^{20}}{y^{-12}}=16x^{20}y^{12}$
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