Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 5 - Exponents and Polynomials - Chapter 5 Test: 18

Answer

$\frac{21}{16}$

Work Step by Step

Recall the following rule: $(\frac{a}{b})^{-x}$ = $\frac{b^{x}}{a^{x}}$. Thus, we obtain: $4^{-2}$ + $4^{-1}$ + $4^{0}$ = $\frac{1^{2}}{4^{2}}$ + $\frac{1^{1}}{4^{1}}$ + $\frac{1^{0}}{4^{0}}$ = $\frac{1}{16}$ + $\frac{1}{4}$ + 1 = Make all the denominators equal. $\frac{1}{16}$ + $\frac{1}{4}$ $\times$ $\frac{4}{4}$ + 1 $\times$ $\frac{16}{16}$ = $\frac{1}{16}$ + $\frac{4}{16}$ + $\frac{16}{16}$ = $\frac{21}{16}$
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