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: 98

Answer

$\sqrt[15]{(2x+1)^{4}}$

Work Step by Step

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