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: 21

Answer

$x^2y$

Work Step by Step

We use the rules of exponents and radicals to obtain: $\displaystyle \sqrt[4]{\frac{x^{9}y^7}{xy^3}}=\sqrt[4]{x^{9-1}y^{7-3}}=\sqrt[4]{x^8y^4}=(x^{8}y^{4})^{1/4}=(x^{8})^{1/4}(y^{4})^{1/4}=x^2y^1=x^2y$
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