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: 43

Answer

$\dfrac{1}{8}$

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: $=\dfrac{1}{16^{\frac{3}{4}}} \\=\dfrac{1}{\sqrt[4]{16^3}} \\=\dfrac{1}{\sqrt[4]{(2^4)^3}} \\=\dfrac{1}{\sqrt[4]{2^{12}}} \\=\dfrac{1}{\sqrt[4]{(2^{3})^4}} \\=\dfrac{1}{2^3} \\=\dfrac{1}{8}$
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