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 - Page 449: 85



Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the Distributive Property and the laws of exponents to simplify the given expression, $ k^{1/4} \left( k^{3/2}-k^{1/2} \right) .$ $\bf{\text{Solution Details:}}$ Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to \begin{array}{l}\require{cancel} k^{1/4}(k^{3/2})+k^{1/4}(-k^{1/2}) .\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} k^{\frac{1}{4}+{\frac{3}{2}}}-k^{\frac{1}{4}+\frac{1}{2}} .\end{array} Changing the rational exponents to similar fractions results to \begin{array}{l}\require{cancel} k^{\frac{1}{4}+{\frac{6}{4}}}-k^{\frac{1}{4}+\frac{2}{4}} \\\\= k^{\frac{7}{4}}-k^{\frac{3}{4}} \\\\= k^{7/4}-k^{3/4} .\end{array}
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