College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter R - Section R.8 - nth Roots; Rational Exponents - R.8 Assess Your Understanding: 22

Answer

$3^{-1}x^{-1}=\frac{1}{3x}$

Work Step by Step

We use the rules of exponents and radicals to obtain: $\displaystyle \sqrt[3]{\frac{3xy^2}{81x^4y^2}}=\sqrt[3]{\frac{1}{27}x^{1-4}y^{2-2}}=\sqrt[3]{27^{-1}x^{-3}y^0}=\sqrt[3]{(3^{-3})x^{-3}}=3^{-1}x^{-1}=\frac{1}{3x}$
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