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: 47

Answer

$a)$ $2ab\sqrt[6]{b}$ $b)$ $4a^{2}\sqrt[3]{b^{2}}$

Work Step by Step

$a)$ $\sqrt[6] {64a^{6}b^{7}}$ $\sqrt[6] {64a^{6}b^{7}}=(\sqrt[6] {64})(\sqrt[6]{a^{6}})(\sqrt[6]{b^{7}})=(2)(a)(b\sqrt[6]{b})=2ab\sqrt[6]{b}$ $b)$ $\sqrt[3]{a^{2}b}\sqrt[3]{64a^{4}b}$ $\sqrt[3]{a^{2}b}\sqrt[3]{64a^{4}b}=\sqrt[3]{(a^{2}b)(64a^{4}b)}=\sqrt[3]{64a^{6}b^{2}}=(\sqrt[3]{64})(\sqrt[3]{a^{6}})(\sqrt[3]{b^{2}})$ $...=(4)(a^{2})(\sqrt[3]{b^{2}})=4a^{2}\sqrt[3]{b^{2}}$
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