Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Review - Exercises - Page 134: 20


$a)$ $\dfrac{4r^{5/2}}{s^{7}}$ $b)$ $\dfrac{4a^{4}c^{6}}{b^{12}}$

Work Step by Step

$a)$ $\dfrac{8r^{1/2}s^{-3}}{2r^{-2}s^{4}}$ Evaluate the division: $\dfrac{8r^{1/2}s^{-3}}{2r^{-2}s^{4}}=\dfrac{8}{2}r^{1/2+2}s^{-3-4}=4r^{5/2}s^{-7}=...$ Take $s^{-7}$ to the denominator to change the sign of its exponent: $...=\dfrac{4r^{5/2}}{s^{7}}$ $b)$ $\Big(\dfrac{ab^{2}c^{-3}}{2a^{3}b^{-4}}\Big)^{-2}$ Evaluate the power: $\Big(\dfrac{ab^{2}c^{-3}}{2a^{3}b^{-4}}\Big)^{-2}=\dfrac{a^{-2}b^{-4}c^{6}}{2^{-2}a^{-6}b^{8}}=...$ Evaluate the division and simplify: $...=\dfrac{1}{2^{-2}}a^{-2+6}b^{-4-8}c^{6}=(2^{2})a^{4}b^{-12}c^{6}=\dfrac{4a^{4}c^{6}}{b^{12}}$
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