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: 83



Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the Distributive Property and the laws of exponents to simplify the given expression, $ p^{2/3} \left( p^{1/3}+2p^{4/3} \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} p^{2/3}(p^{1/3})+p^{2/3}(2p^{4/3}) .\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} p^{\frac{2}{3}+\frac{1}{3}}+2p^{\frac{2}{3}+\frac{4}{3}} \\\\= p^{\frac{3}{3}}+2p^{\frac{6}{3}} \\\\= p^{1}+2p^{2} \\\\= p+2p^{2} .\end{array}
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