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: 86


$\displaystyle \frac{8}{x^{3}y}$

Work Step by Step

We simplify: $\displaystyle \frac{(4x^{-1}y^{1/3})^{3/2}}{(xy)^{3/2}}=\frac{4^{3/2}(x^{-1})^{3/2}(y^{1/3})^{3/2}}{x^{3/2}y^{3/2}}= \frac{(4^{1/2})^{3}x^{-3/2}y^{1/2}}{ x^{3/2}y^{3/2}}=2^{3}x^{-3/2-3/2}y^{1/2-3/2}=8x^{-6/2}y^{-2/2}=8x^{-3}y^{-1}=\frac{8}{x^{3}y}$
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