Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 5 - Number Theory and the Real Number System - 5.6 Exponents and Scientific Notation - Exercise Set 5.6: 31

Answer

$\dfrac{1}{x^{16}}$

Work Step by Step

(i) $a^m \cdot a^n = a^{m+n}$ (ii) $\dfrac{a^m}{a^n}=a^{m-n}$ (iii) $a^{-m} = \dfrac{1}{a^m}, a \ne 0, m \gt0$ (iv) $(a^m)^n=a^{mn}$ Use rule (i) to find: $=(x^{5+3})^{-2} \\=(x^8)^{-2}$ Use rule (iv) to find: $=x^{8(-2)} \\=x^{-16}$ Use rule (iii) to find: $=\dfrac{1}{x^{16}}$
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