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: 38

Answer

$\dfrac{1}{32}$

Work Step by Step

RECALL: (i) $\left(\dfrac{x}{y}\right)^n=\dfrac{x^n}{y^n}, y \ne 0$ (ii) $(xy)^m = x^my^m$ (iii) $(a^m)^n=a^{mn}$ (iv) $\dfrac{a^m}{a^n} = a^{m-n}$ Use the rules above to have: $=(2^{2-3})^5 \\=(2^{-1})^5 \\=2^{-1(5)} \\=2^{-5} \\=\dfrac{1}{2^5} \\=\dfrac{1}{32}$
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