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: 44

Answer

$\sqrt[4]{27p^{3}}-\sqrt[3]{4x}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the definition of rational exponents to convert the given expression, $ (3p)^{3/4}-(4x)^{1/3} ,$ to radical form. Then use the laws of exponents to simplify the resulting expression. $\bf{\text{Solution Details:}}$ Using the definition of rational exponents which is given by $a^{\frac{m}{n}}=\sqrt[n]{a^m}=\left(\sqrt[n]{a}\right)^m,$ the expression above is equivalent to \begin{array}{l}\require{cancel} \sqrt[4]{(3p)^{3}}-\sqrt[3]{(4x)^{1}} .\end{array} Using the extended Power Rule of the laws of exponents which is given by $\left( x^my^n \right)^p=x^{mp}y^{np},$ the expression above is equivalent to \begin{array}{l}\require{cancel} \sqrt[4]{3^3p^{3}}-\sqrt[3]{4^1x^{1}} \\\\= \sqrt[4]{27p^{3}}-\sqrt[3]{4x} .\end{array}
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