College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.6 - Rational Exponents - R.6 Exercises - Page 58: 116

Answer

$8$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given expression, $ \dfrac{20^{3/2}}{5^{3/2}} ,$ use the laws of exponents. $\bf{\text{Solution Details:}}$ Using the extended Power Rule of the laws of exponents which states that $\left( \dfrac{x^m}{z^p} \right)^q=\dfrac{x^{mq}}{z^{pq}},$ the expression above is equivalent to\begin{array}{l}\require{cancel} \left(\dfrac{20}{5}\right)^{3/2} \\\\= 4^{3/2} .\end{array} 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})^{3} \\\\= (2)^{3} \\\\= 8 .\end{array}
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