To simplify \( \frac{3^2}{3^{-2}} \), we can use the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \).
So we can write:
\[ \frac{3^2}{3^{-2}} = 3^{2 - (-2)} = 3^{2 + 2} = 3^4 \]
Now, \( 3^4 = 81 \).
Therefore, any expression that simplifies to \( 3^4 \) or 81 is equivalent to \( \frac{3^2}{3^{-2}} \).
Here are some equivalent expressions:
- \( 3^4 \)
- \( 81 \)
- \( 3^2 \times 3^2 \)
- \( (3^2)^2 \)
- \( 9 \times 9 \)
If you have a list of expressions, you can check which of them align with these forms.