Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 5 - Section 5.2 - Negative Exponents and Scientific Notation - Exercise Set: 8

Answer

$\frac{5}{16}$

Work Step by Step

We know that $a^{−n}=\frac{1}{a^{n}}$ and $\frac{1}{a^{-n}}=a^{n}$ (as long as a is a nonzero real number and n is an integer). Therefore, $4^{-1}+4^{-2}=\frac{1}{4}+\frac{1}{4^{2}}=\frac{1}{4}+\frac{1}{16}=\frac{1\times4}{4\times4}+\frac{1}{16}=\frac{4}{16}+\frac{1}{16}=\frac{4+1}{16}=\frac{5}{16}$.
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