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: 78

Answer

$a)$ $s^{5/4}$ $b)$ $\dfrac{3y}{x}$

Work Step by Step

$a)$ $\sqrt{s\sqrt{s^{3}}}$ Rewrite the roots as powers with rational exponent: $\sqrt{s\sqrt{s^{3}}}=(s\cdot s^{3/2})^{1/2}=...$ Evaluate the product inside the parentheses: $...=(s^{1+3/2})^{1/2}=(s^{5/2})^{1/2}=...$ Finally, evaluate the power: $...=s^{5/4}$ $b)$ $\sqrt[3]{\dfrac{54x^{2}y^{4}}{2x^{5}y}}$ Rewrite the cubic root as a power with rational exponent: $\sqrt[3]{\dfrac{54x^{2}y^{4}}{2x^{5}y}}=\Big(\dfrac{54x^{2}y^{4}}{2x^{5}y}\Big)^{1/3}=...$ Evaluate the division inside the parentheses: $...=(27x^{2-5}y^{4-1})^{1/3}=(27x^{-3}y^{3})^{1/3}=...$ Finally, evaluate the power and simplify if possible: $...=3x^{-1}y=\dfrac{3y}{x}$
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