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: 41

Answer

$a)$ $\dfrac{8a^{3}b^{-4}}{2a^{-5}b^{5}}=\dfrac{4a^{8}}{b^{9}}$ $b)$ $\Big(\dfrac{y}{5x^{-2}}\Big)^{-3}=\dfrac{125}{x^{6}y^{3}}$

Work Step by Step

$a)$ $\dfrac{8a^{3}b^{-4}}{2a^{-5}b^{5}}$ $\dfrac{8a^{3}b^{-4}}{2a^{-5}b^{5}}=\dfrac{8}{2}a^{3-(-5)}b^{-4-5}=4a^{8}b^{-9}=\dfrac{4a^{8}}{b^{9}}$ $b)$ $\Big(\dfrac{y}{5x^{-2}}\Big)^{-3}$ $\Big(\dfrac{y}{5x^{-2}}\Big)^{-3}=\Big(\dfrac{5x^{-2}}{y}\Big)^{3}=\dfrac{125x^{-6}}{y^{3}}=\dfrac{125}{x^{6}y^{3}}$
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