To find the equivalent expression for \( 3^{-4} \), we can use the property of exponents that states \( a^{-n} = \frac{1}{a^{n}} \).
Applying this property:
\[ 3^{-4} = \frac{1}{3^{4}} \]
Now, we can calculate \( 3^{4} \):
\[ 3^{4} = 3 \times 3 \times 3 \times 3 \]
Calculating step by step:
- \( 3 \times 3 = 9 \)
- \( 9 \times 3 = 27 \)
- \( 27 \times 3 = 81 \)
So, \( 3^{4} = 81 \).
Now we have:
\[ 3^{-4} = \frac{1}{3^{4}} = \frac{1}{81} \]
Thus, \( 3^{-4} \) is equivalent to \( \frac{1}{81} \).