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: 83

Answer

$x^{2/3}y$

Work Step by Step

We simplify: $\displaystyle \frac{(x^{2}y)^{1/3}(xy^{2})^{2/3}}{x^{2/3}y^{2/3}}=\frac{(x^{2})^{1/3}(y)^{1/3}(x)^{2/3}(y^{2})^{2/3}}{x^{2/3}y^{2/3}}=\frac{x^{2/3}y^{1/3}x^{2/3}y^{4/3}}{x^{2/3}y^{2/3}}=x^{2/3+2/3-2/3}y^{1/3+4/3-2/3}=x^{2/3}y^{3/3}=x^{2/3}y$
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