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: 77

Answer

$=2xyz\sqrt[4]{x^{2}z^{3}}$.

Work Step by Step

The given expression is $\sqrt[4]{8x^2y^3z^6}\cdot \sqrt[4] {2x^4yz}$ Apply product rule $\sqrt[n] a \cdot \sqrt[n] b = \sqrt[n] {ab}$ $\sqrt[4]{8x^2y^3z^6\cdot 2x^4yz}$ $\sqrt[4]{2^3x^2y^3z^6\cdot 2^1x^4y^1z^1}$ Use $a^n\cdot a^m = a^{m+n}$ $\sqrt[4]{2^{3+1}x^{2+4}y^{3+1}z^{6+1}}$ $\sqrt[4]{2^{4}x^{6}y^{4}z^{7}}$ Further simplify by using product rule. $=\sqrt[4]{2^{4}x^{4+2}y^{4}z^{4+3}}$ $=\sqrt[4]{2^{4}x^{4}x^{2}y^{4}z^{4}z^{3}}$ $=\sqrt[4]{(2xyz)^4x^{2}z^{3}}$ $=2xyz\sqrt[4]{x^{2}z^{3}}$.
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