## College Algebra (10th Edition)

Published by Pearson

# Chapter 6 - Section 6.3 - Exponential Functions - 6.3 Assess Your Understanding: 12

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#### Work Step by Step

RECALL: (1) $\dfrac{1}{a^x} = a^{-x}$ (2) $(a^m)^n=a^{mn}$ Use rule (1) above to obtain: $\left(\dfrac{1}{3}\right)^x = \left(3^{-1}\right)^x$ Use rule (2) above to obtain: $\left(3^{-1}\right)^x = 3^{-1(x)} = 3^{-x}$ Note that $3^x \ne 3^{-x}$, so $y=3^x$ is not equivalent to $y=\left(\dfrac{1}{3}\right)^x$. This means that they have different graphs. Thus, the given statement is false.

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