Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 5 - Section 5.2 - Negative Exponents and Scientific Notation - Practice: 15

Answer

$-\frac{4x^{2}}{y^{4}}$

Work Step by Step

We know that $a^{−n}=\frac{1}{a^{n}}$ and $\frac{1}{a^{-n}}=a^{n}$ (as long as a is a nonzero real number and n is an integer). Therefore, $-\frac{32x^{-3}y^{-6}}{8x^{-5}y^{-2}}=-\frac{32}{8}\times x^{-3-(-5)}\times y^{-6-(-2)}=-4\times x^{2}\times y^{-4}=-4\times x^{2}\times\frac{1}{y^{4}}=-\frac{4x^{2}}{y^{4}}$.
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