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 - Page 30: 79



Work Step by Step

RECALL: (i) $a^{-m} = \dfrac{1}{a^m},a\ne0$ (ii) $\sqrt[n]{a^m} = a^{\frac{m}{n}}$ (iii) $\dfrac{a^m}{a^n} = a^{m-n}, a\ne0$ Simplify the radicand by canceling common factors: $\require{cancel} =\sqrt{\dfrac{16\cancel{u^3}u^2\cancel{v}}{\cancel{u}\cancel{v^{5}v^4}}} \\=\sqrt{\dfrac{16u^2}{v^4}}$ Factor the radicand so that at least one factor is a perfect square to obtain: $\\=\sqrt{\dfrac{(4u)^2}{(v^2)^2}}$ Simplify to obtain: $=\dfrac{4u}{v^2}$
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