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 - Page 23: 74

Answer

$a)$ $b^{5/4}$ $b)$ $2a^{7/6}$

Work Step by Step

$a)$ $\sqrt[4]{b^{3}}\sqrt{b}$ Rewrite the radical expressions as powers with rational exponent: $\sqrt[4]{b^{3}}\sqrt{b}=b^{3/4}\cdot b^{1/2}=...$ Evaluate the product: $...=b^{3/4+1/2}=b^{5/4}$ $b)$ $(2\sqrt{a})(\sqrt[3]{a^{2}})$ Rewrite the radical expressions as powers with rational exponent: $(2\sqrt{a})(\sqrt[3]{a^{2}})=(2a^{1/2})(a^{2/3})=...$ Evaluate the product: $...=2a^{1/2+2/3}=2a^{7/6}$
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