Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.2 - Rational Exponents - Exercise Set: 47

Answer

$\dfrac{3}{2}$

Work Step by Step

RECALL: (i) $a^{-\frac{m}{n}}=\dfrac{1}{a^{\frac{m}{n}}}$ (ii) $a^{\frac{m}{n}}=\sqrt[n]{a^m}$ Use the rules above to obtain: $=\dfrac{1}{(\frac{8}{27})^{\frac{1}{3}}} \\=\dfrac{1}{\sqrt[3]{\dfrac{8}{27}}} \\=\dfrac{1}{\sqrt[3]{\left(\dfrac{2}{3}\right)^3}} \\=\dfrac{1}{\frac{2}{3}} \\=1 \cdot \dfrac{3}{2} \\=\dfrac{3}{2}$
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