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: 75

Answer

$a)$ $2st^{11/6}$ $b)$ $x$

Work Step by Step

$a)$ $\sqrt{4st^{3}}\sqrt[6]{s^{3}t^{2}}$ Take the square root of $4$ and write the radical expressions as powers with rational exponent: $\sqrt{4st^{3}}\sqrt[6]{s^{3}t^{2}}=(2s^{1/2}t^{3/2})(s^{1/2}t^{1/3})=...$ Evaluate the product: $...=2s^{1/2+1/2}t^{3/2+1/3}=2st^{11/6}$ $b)$ $\dfrac{\sqrt[4]{x^{7}}}{\sqrt[4]{x^{3}}}$ Rewrite the radical expressions as powers with rational exponent: $\dfrac{\sqrt[4]{x^{7}}}{\sqrt[4]{x^{3}}}=\dfrac{x^{7/4}}{x^{3/4}}=...$ Evaluate the division: $...=x^{7/4-3/4}=x^{4/4}=x$
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