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 - Exercise Set: 67

Answer

$\dfrac{(-2xy^{-3})^{-3}}{(xy^{-1})^{-1}}=-\dfrac{y^{8}}{8x^{2}}$

Work Step by Step

$\dfrac{(-2xy^{-3})^{-3}}{(xy^{-1})^{-1}}$ Evaluate the exponential expressions in the numerator and the denominator: $\dfrac{(-2xy^{-3})^{-3}}{(xy^{-1})^{-1}}=\dfrac{(-2)^{-3}x^{-3}y^{9}}{x^{-1}y}=...$ Evaluate the division and simplify: $...=\dfrac{1}{(-2)^{3}}x^{-3-(-1)}y^{9-1}=\dfrac{1}{-8}x^{-2}y^{8}=-\dfrac{y^{8}}{8x^{2}}$
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