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: 73


$\displaystyle \frac{27\sqrt{2}}{32}$

Work Step by Step

We simplify: $(\displaystyle \frac{8}{9})^{-3/2}=(\frac{9}{8})^{3/2}=((\frac{9}{8})^{1/2})^3=(\sqrt{\frac{9}{8}})^{3}=(\frac{3}{2\sqrt{2}})^{3} =\frac{3^{3}}{2^{3}(\sqrt{2})^{3}}=\frac{27}{8*2\sqrt{2}}=\frac{27}{16\sqrt{2}} =\frac{27}{16\sqrt{2}}*\frac{\sqrt{2}}{\sqrt{2}}=\frac{27\sqrt{2}}{16*2}=\frac{27\sqrt{2}}{32}$
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