Algebra 1

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

Chapter 7 - Exponents and Exponential Functions - 7-5 Division Properties of Exponents - Practice and Problem-Solving Exercises: 42

Answer

$\dfrac{256}{625}$

Work Step by Step

(i) $a^{-m} = \dfrac{1}{a^m}, a\ne0$ (ii) $\left(\dfrac{a}{b}\right)^m=\dfrac{a^m}{b^m}, b \ne0$ Use the rules above to obtain: $=\dfrac{1}{(\frac{5}{4})^4} \\=\dfrac{1}{\frac{5^4}{4^4}} \\=1 \cdot \dfrac{4^4}{5^4} \\=\dfrac{4^4}{5^4} \\=\dfrac{256}{625}$
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