To simplify \( 3^{-4} \) using the property of negative integer exponents, we can use the fact that:
\[ a^{-n} = \frac{1}{a^n} \]
Applying this property to \( 3^{-4} \):
\[ 3^{-4} = \frac{1}{3^{4}} \]
Now we calculate \( 3^{4} \):
\[ 3^{4} = 3 \times 3 \times 3 \times 3 = 81 \]
Thus, we have:
\[ 3^{-4} = \frac{1}{81} \]
The final answer, without any exponent expression or decimals, is
\(\frac{1}{81}\).