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: 80

Answer

$2xy^2z^2\sqrt[5]{2y^{2}z}$.

Work Step by Step

The given expression is $\sqrt[5]{8x^4y^3z^3}\cdot \sqrt[5] {8xy^9z^8}$ Apply product rule $\sqrt[n] a \cdot \sqrt[n] b = \sqrt[n] {ab}$ $\sqrt[5]{8x^4y^3z^3\cdot 8xy^9z^8}$ $\sqrt[5]{2^3x^4y^3z^3\cdot 2^3x^1y^9z^8}$ Use $a^n\cdot a^m = a^{m+n}$ $\sqrt[5]{2^{3+3}x^{4+1}y^{3+9}z^{3+8}}$ $\sqrt[5]{2^{6}x^{5}y^{12}z^{11}}$ Further simplify by using product rule. $=\sqrt[5]{2^{5+1}x^{5}y^{5+5+2}z^{5+5+1}}$ $=\sqrt[5]{2^{5}2^1x^{5}y^{5}y^{5}y^{2}z^{5}z^{5}z^{1}}$ $=\sqrt[5]{(2xyyzz)^52y^{2}z}$ $=2xyyzz\sqrt[5]{2y^{2}z}$. $=2xy^2z^2\sqrt[5]{2y^{2}z}$.
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