Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - 10.5 Expressions Containing Several Radical Terms - 10.5 Exercise Set - Page 661: 93



Work Step by Step

Using the same indices for the radicals, the given expression, $ \dfrac{\sqrt[]{ab^3}}{\sqrt[5]{a^2b^3}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\sqrt[2(5)]{a^{1(5)}b^{3(5)}}}{\sqrt[5(2)]{a^{2(2)}b^{3(2)}}} \\\\= \dfrac{\sqrt[10]{a^{5}b^{15}}}{\sqrt[10]{a^{4}b^{6}}} \\\\= \sqrt[10]{\dfrac{a^{5}b^{15}}{a^{4}b^{6}}} \\\\= \sqrt[10]{a^{5-4}b^{15-6}} \\\\= \sqrt[10]{a^{1}b^{9}} \\\\= \sqrt[10]{ab^{9}} \end{array} * Note that it is assumed that all variables represent positive numbers.
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