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: 68

Answer

$a)$ $\dfrac{2y^{4/3}}{x^{2}}$ $b)$ $\dfrac{t^{1/4}}{2s^{1/2}}$

Work Step by Step

$a)$ $\Big(\dfrac{x^{8}y^{-4}}{16y^{4/3}}\Big)^{-1/4}$ Invert the fraction to change the sign of its exponent: $\Big(\dfrac{x^{8}y^{-4}}{16y^{4/3}}\Big)^{-1/4}=\Big(\dfrac{16y^{4/3}}{x^{8}y^{-4}}\Big)^{1/4}=...$ Evaluate the power: $...=\dfrac{(16^{1/4})y^{1/3}}{x^{2}y^{-1}}=\dfrac{(\sqrt[4]{16})y^{1/3}}{x^{2}y^{-1}}=\dfrac{2y^{1/3}}{x^{2}y^{-1}}=...$ Evaluate the division and simplify if possible: $...=\dfrac{2y^{1/3-(-1)}}{x^{2}}=\dfrac{2y^{4/3}}{x^{2}}$ $b)$ $\Big(\dfrac{4s^{3}t^{4}}{s^{2}t^{9/2}}\Big)^{-1/2}$ Invert the fraction to change the sign of its exponent: $\Big(\dfrac{4s^{3}t^{4}}{s^{2}t^{9/2}}\Big)^{-1/2}=\Big(\dfrac{s^{2}t^{9/2}}{4s^{3}t^{4}}\Big)^{1/2}=...$ Evaluate the power: $...=\dfrac{st^{9/4}}{(\sqrt{4})s^{3/2}t^{2}}=\dfrac{st^{9/4}}{2s^{3/2}t^{2}}=...$ Evaluate the division and simplify if possible: $...=\dfrac{s^{1-3/2}t^{9/4-2}}{2}=\dfrac{s^{-1/2}t^{1/4}}{2}=\dfrac{t^{1/4}}{2s^{1/2}}$
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