Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 5 Polynomials and Polynomial Functions - 5.1 Use Properties of Exponents - 5.1 Exercises - Skill Practice - Page 334: 47



Work Step by Step

As per the zero property, we have $a^0=1$ Thus, $\dfrac{1}{a^m}=\dfrac{a^0}{a^m}$ ...(1) Now, we need to use the quotient property. $\dfrac{a^0}{a^m}=a^{0-m}=a^{-m}$ Equation (1) becomes: $\dfrac{1}{a^m}=\dfrac{a^0}{a^m}=a^{-m}$ This gives: $a^{-m}=\dfrac{1}{a^m}$ Hence, the result has been verified.
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