Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.3 - Multiplying and Simplifying Radical Expressions - Exercise Set - Page 531: 90

Answer

$40a^4b^2\sqrt [4] {2ab^3}$.

Work Step by Step

The given expression is $=(5a^2b\sqrt [4] {8a^2b})(4ab\sqrt [4]{4a^3b^2})$ Clear the parentheses. $=20a^3b^2\sqrt [4] {8a^2b}\sqrt [4] {4a^3b^2}$ Apply the product rule of radicals. $\sqrt [4]a \cdot \sqrt [4] b = \sqrt [4] {ab}$ $=20a^3b^2\sqrt [4] {8a^2b\cdot 4a^3b^2}$ Find the factors: $=20a^3b^2\sqrt [4] {2^42a^4ab^3}$ Factor into two radicals. $=20a^3b^2\sqrt [4] {2^4a^4}\sqrt [4] {2ab^3}$ Simplify. $=20a^3b^2\cdot 2a\sqrt [4] {2ab^3}$ $=40a^4b^2\sqrt [4] {2ab^3}$.
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