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Question

# Simplify each expression. Assume all variables are nonzero.$3^2 \cdot 3^{-5}$

Solution

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Step 1
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We have to simplify the expression:

\begin{aligned} 3^2 \cdot 3^{-5}&=3^{2+(-5)} & \begin{pmatrix} \text{Product of powers property:}\\ a^n\cdot a^m= a^{n+m} \end{pmatrix} \\ &=3^{2-5}\\ &=3^{-3}\\ &=\frac{1}{3^3} & \begin{pmatrix} \text{Negative exponent property:}\\ a^{-n}= \frac{1}{a^n}\end{pmatrix} \\ &=\frac{1}{27} & (3^3=3\cdot3\cdot3=27). \end{aligned}

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