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: 63

Answer

$a)$ $w^{5/3}$ $b)$ $8a^{13/4}$

Work Step by Step

$a)$ $\dfrac{w^{4/3}w^{2/3}}{w^{1/3}}$ Evaluate the product in the numerator: $\dfrac{w^{4/3}w^{2/3}}{w^{1/3}}=\dfrac{w^{4/3+2/3}}{w^{1/3}}=\dfrac{w^{6/3}}{w^{1/3}}=...$ Evaluate the division: $...=w^{6/3-1/3}=w^{5/3}$ $b)$ $\dfrac{a^{5/4}(2a^{3/4})^{3}}{a^{1/4}}$ Raise each factor of the expression inside the parentheses to the power of $3$: $\dfrac{a^{5/4}(2a^{3/4})^{3}}{a^{1/4}}=\dfrac{a^{5/4}(2^{3})(a^{9/4})}{a^{1/4}}=\dfrac{a^{5/4}(8)(a^{9/4})}{a^{1/4}}=...$ Evaluate the product in the numerator: $...=\dfrac{8a^{5/4+9/4}}{a^{1/4}}=\dfrac{8a^{14/4}}{a^{1/4}}=...$ Finally, evaluate the division: $...=8a^{14/4-1/4}=8a^{13/4}$
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