Intermediate Algebra (12th Edition)

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

Chapter 4 - Section 4.1 - Integer Exponents and Scientific Notation - 4.1 Exercises - Page 277: 72



Work Step by Step

According to the quotient rule for exponents, $\frac{a^{m}}{a^{n}}=a^{m-n}$ (where $a\ne0$). Therefore, $\frac{5^{-4}}{5^{2}}=5^{-4-2}=5^{-6}$. Furthermore, the definition of negative exponents tells us that $a^{-n}=\frac{1}{a^{n}}$. Therefore, $5^{-6}=\frac{1}{5^{6}}$.
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