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: 42


$a)$ $\dfrac{5xy^{-2}}{x^{-1}y^{-3}}=5x^{2}y$ $b)$ $\Big(\dfrac{2a^{-1}b}{a^{2}b^{-3}}\Big)^{-3}=\dfrac{a^{9}}{8b^{12}}$

Work Step by Step

$a)$ $\dfrac{5xy^{-2}}{x^{-1}y^{-3}}$ $\dfrac{5xy^{-2}}{x^{-1}y^{-3}}=5x^{1-(-1)}y^{-2-(-3)}=5x^{2}y$ $b)$ $\Big(\dfrac{2a^{-1}b}{a^{2}b^{-3}}\Big)^{-3}$ $\Big(\dfrac{2a^{-1}b}{a^{2}b^{-3}}\Big)^{-3}=\Big(\dfrac{a^{2}b^{-3}}{2a^{-1}b}\Big)^{3}=\dfrac{a^{6}b^{-9}}{8a^{-3}b^{3}}=\dfrac{1}{8}a^{6-(-3)}b^{-9-3}=...$ $...=\dfrac{1}{8}a^{9}b^{-12}=\dfrac{a^{9}}{8b^{12}}$
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