Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 7 - Section 7.2 - Rational Exponents - 7.2 Exercises: 89



Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the Distributive Property and the laws of exponents to simplify the given expression, $ -5x^{7/6}(x^{5/6}-x^{-1/6}) .$ $\bf{\text{Solution Details:}}$ Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to \begin{array}{l}\require{cancel} -5x^{7/6}(x^{5/6})-5x^{7/6}(-x^{-1/6}) .\end{array} Using the Product Rule of the laws of exponents which is given by $x^m\cdot x^n=x^{m+n},$ the expression above is equivalent to \begin{array}{l}\require{cancel} -5x^{\frac{7}{6}+\frac{5}{6}}+5x^{\frac{7}{6}+\left(-\frac{1}{6} \right)} \\\\= -5x^{\frac{7}{6}+\frac{5}{6}}+5x^{\frac{7}{6}-\frac{1}{6}} \\\\= -5x^{\frac{12}{6}}+5x^{\frac{6}{6}} \\\\= -5x^{2}+5x^{1} \\\\= -5x^{2}+5x .\end{array}
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