Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 7 - Exponents and Exponential Functions - 7-4 More Multiplication Properties of Exponents - Practice and Problem-Solving Exercises - Page 437: 33


$\frac {p^{15}}{q^{9}}$

Work Step by Step

Given expression : $p(p^{-7}q^{3})^{-2}q^{-3}$ Now, $(ab)^{n}=a^{n}b^{n}$ Hence, $(p^{-7}q^{3})^{-2} = (p^{-7})^{-2}$ X $(q^{3})^{-2}=p^{14}$ X $q^{-6}$ The expression becomes : $p$ X $p^{14}$ X $q^{-6}$ X $q^{-3}=p^{1+14}$ X $q^{-6-3}$ (since the exponents are added while multipliying with the same base) This becomes : $p^{15}$ X $q^{-9}$ Final result : $\frac {p^{15}}{q^{9}}$ (since $a^{-n}=\frac{1}{a^{n}}$)
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