To solve \( 3^{-4} \) using the Property of Negative Integer Exponents, we start by applying the property which states that \( a^{-n} = \frac{1}{a^n} \).
Thus, we can rewrite \( 3^{-4} \) as:
\[ 3^{-4} = \frac{1}{3^4} \]
Next, we calculate \( 3^4 \):
\[ 3^4 = 3 \times 3 \times 3 \times 3 = 81 \]
Now, substituting this value back, we have:
\[ 3^{-4} = \frac{1}{3^4} = \frac{1}{81} \]
Therefore, the final answer is:
\[ \frac{1}{81} \]
This result does not contain any exponent expressions or decimals.