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: 68

Answer

$\dfrac{(-3x^{2}y^{2})^{-2}}{(xyz)^{-2}}=\dfrac{z^{2}}{9x^{2}y^{2}}$

Work Step by Step

$\dfrac{(-3x^{2}y^{2})^{-2}}{(xyz)^{-2}}$ Evaluate the exponential expressions in the numerator and the denominator: $\dfrac{(-3x^{2}y^{2})^{-2}}{(xyz)^{-2}}=\dfrac{(-3)^{-2}x^{-4}y^{-4}}{x^{-2}y^{-2}z^{-2}}=...$ Evaluate the division and simplify: $...=\dfrac{1}{(-3)^{2}}\cdot\dfrac{x^{-4-(-2)}y^{-4-(-2)}}{z^{-2}}=\dfrac{1}{9}\cdot\dfrac{x^{-2}y^{-2}}{z^{-2}}=\dfrac{z^{2}}{9x^{2}y^{2}}$
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