Which expression is equivalent to 3^2⋅ 3−5?

Group of answer choices

fraction 1 over 3 to the power negative 7

fraction 1 over 3 to the power negative 3

fraction 1 over 3 to the power 3

fraction 1 over 3 to the power 7

1 answer

To simplify the expression \( 3^2 \cdot 3^{-5} \), we can use the property of exponents which states that \( a^m \cdot a^n = a^{m+n} \).

In this case:

\[ 3^2 \cdot 3^{-5} = 3^{2 + (-5)} = 3^{-3} \]

Now, we can express \( 3^{-3} \) in terms of a fraction:

\[ 3^{-3} = \frac{1}{3^3} \]

Thus, the expression \( 3^2 \cdot 3^{-5} \) simplifies to \( \frac{1}{3^3} \).

Based on the answer choices, the equivalent expression is:

fraction \( 1 \) over \( 3 \) to the power \( 3 \).