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: 65

Answer

$a)$ $4a^{4}b$ $b)$ $8a^{9}b^{12}$

Work Step by Step

$a)$ $(8a^{6}b^{3/2})^{2/3}$ Raise each factor inside the parentheses to the power of $\dfrac{2}{3}$ and simplify: $(8a^{6}b^{3/2})^{2/3}=(8^{2/3})a^{4}b=(\sqrt[3]{8^{2}})a^{4}b=4a^{4}b$ $b)$ $(4a^{6}b^{8})^{3/2}$ Raise each factor inside the parentheses to the power of $\dfrac{3}{2}$ and simplify: $(4a^{6}b^{8})^{3/2}=(4^{3/2})a^{9}b^{12}=(\sqrt{4^{3}})a^{9}b^{12}=8a^{9}b^{12}$
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