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: 87

Answer

$a^{2}b^{2}c^{2}\sqrt[6]{a^2bc^2}$

Work Step by Step

Using the same indices for the radicals, the given expression, $ \sqrt[]{a^4b^3c^4}\sqrt[3]{ab^2c} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt[2(3)]{a^{4(3)}b^{3(3)}c^{4(3)}}\cdot\sqrt[3(2)]{a^{1(2)}b^{2(2)}c^{1(2)}} \\\\= \sqrt[6]{a^{12}b^{9}c^{12}}\cdot\sqrt[6]{a^{2}b^{4}c^{2}} \\\\= \sqrt[6]{a^{12}b^{9}c^{12}(a^{2}b^{4}c^{2})} \\\\= \sqrt[6]{a^{12+2}b^{9+4}c^{12+2}} \\\\= \sqrt[6]{a^{14}b^{13}c^{14}} \\\\= \sqrt[6]{a^{12}b^{12}c^{12}\cdot a^2bc^2} \\\\= \sqrt[6]{(a^{2}b^{2}c^{2})^6\cdot a^2bc^2} \\\\= a^{2}b^{2}c^{2}\sqrt[6]{a^2bc^2} \end{array} * Note that it is assumed that all variables represent positive numbers.
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