Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 4 - Review Exercises: 21

Answer

$\dfrac{10p^{8}}{q^7}$

Work Step by Step

Use the laws of exponents to simplify the given expression, $ \dfrac{(5p^{-2}q)(4p^5q^{-3})}{2p^{-5}q^5} .$ Using the Product Rule of the laws of exponents which states that $x^m\cdot x^n=x^{m+n},$ the expression above simplifies to \begin{array}{l}\require{cancel} \dfrac{(5)(4)p^{-2+5}q^{1+(-3)}}{2p^{-5}q^5} \\\\= \dfrac{20p^{3}q^{-2}}{2p^{-5}q^5} .\end{array} Using the Quotient Rule of the laws of exponents which states that $\dfrac{x^m}{x^n}=x^{m-n},$ the expression above simplifies to \begin{array}{l}\require{cancel} 10p^{3-(-5)}q^{-2-5} \\\\= 10p^{3+5}q^{-2-5} \\\\= 10p^{8}q^{-7} .\end{array} Using the Negative Exponent Rule of the laws of exponents which states that $x^{-m}=\dfrac{1}{x^m}$ or $\dfrac{1}{x^{-m}}=x^m,$ the expression above is equivalent to \begin{array}{l}\require{cancel} \dfrac{10p^{8}}{q^7} .\end{array}
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