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 7.2 - Rational Exponents - Exercise Set - Page 522: 97

Answer

$\sqrt[12] { a^{ 10}b^{7} } $.

Work Step by Step

The given expression is $\sqrt[4] {a^2b} \cdot \sqrt[3] {ab}$ Use $\sqrt[n] x=x^{\frac{1}{n}}$. $=\left ( a^2b \right )^{\frac{1}{4}} \cdot \left ( ab \right )^{\frac{1}{3}}$ Use $(ab)^m=a^mb^m$. $= a^{2\cdot \frac{1}{4} }b^{\frac{1}{4}} \cdot a^{\frac{1}{3}}b ^{\frac{1}{3}}$ $= a^{ \frac{1}{2} }b^{\frac{1}{4}} \cdot a^{\frac{1}{3}}b ^{\frac{1}{3}}$ Use $a^m\cdot a^n=a^{m+n}$ $= a^{ \frac{1}{2}+\frac{1}{3} }b^{\frac{1}{4}+\frac{1}{3}} $ $= a^{ \frac{3+2}{6}}b^{\frac{3+4}{12}} $ $= a^{ \frac{5}{6}}b^{\frac{7}{12}} $. $= a^{ \frac{10}{12}}b^{\frac{7}{12}} $. $= \left ( a^{ 10}b^{7} \right )^{\frac{1}{12}} $. Use $x^{\frac{1}{n}}=\sqrt[n] x$. $=\sqrt[12] { a^{ 10}b^{7} } $.
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