Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.2 - Exponents and Radicals - 1.2 Exercises: 57

Answer

$a)$ $4$ $b)$ $\dfrac{3}{2}$ $c)$ $\dfrac{8}{27}$

Work Step by Step

$a)$ $32^{2/5}$ Rewrite the expression as a radical expression and evaluate: $32^{2/5}=\sqrt[5]{32^{2}}=\sqrt[5]{1024}=4$ $b)$ $\Big(\dfrac{4}{9}\Big)^{-1/2}$ Switch the numerator and the denominator and change the sign of the exponent: $\Big(\dfrac{4}{9}\Big)^{-1/2}=\Big(\dfrac{9}{4}\Big)^{1/2}=...$ Rewrite as a radical expression and evaluate: $...=\sqrt{\dfrac{9}{4}}=\dfrac{3}{2}$ $c)$ $\Big(\dfrac{16}{81}\Big)^{3/4}$ Rewrite this as a radical expression and evaluate: $\Big(\dfrac{16}{81}\Big)^{3/4}=\sqrt[4]{\Big(\dfrac{16}{81}\Big)^{3}}=\sqrt[4]{\dfrac{4096}{531441}}=\dfrac{8}{27}$
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