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 - Page 79: 85


$\displaystyle \frac{8x^{5/4}}{y^{3/4}}$

Work Step by Step

We simplify: $\displaystyle \frac{(16x^{2}y^{-1/3})^{3/4}}{(xy^2)^{1/4}}=\frac{16^{3/4}(x^{2})^{3/4}(y^{-1/3})^{3/4}}{x^{1/4}(y^{2})^{1/4}} =\frac{(16^{1/4})^{3}x^{3/2}y^{-1/4}}{x^{1/4}y^{2/4}}=2^{3}x^{3/2-1/4}y^{-1/4-2/4}=8x^{5/4}y^{-3/4}=\frac{8x^{5/4}}{y^{3/4}}$
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