College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Section P.4 - Rational Exponents and Radicals - P.4 Exercises: 12

Answer

$\dfrac{1}{10\sqrt{10}}$

Work Step by Step

RECALL: (i) $a^{\frac{m}{n}} =\sqrt[n]{a^m}$ (i) $a^{-m} = \dfrac{1}{a^m}, a\ne0$ Use rule (ii) above to obtain: $=\dfrac{1}{a^{\frac{3}{2}}}$ Use rule (i) above, where m=3 and n=2, to obtain: $=\dfrac{1}{\sqrt{10^3}}$ Factor the radicand so that one factor is a square, then simplify to obtain: $=\dfrac{1}{\sqrt{10^2 \cdot 10}} \\=\dfrac{1}{10\sqrt{10}}$
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