To evaluate \( 4^{-4} \), we use the property of negative exponents, which states that \( a^{-n} = \frac{1}{a^n} \).
Applying this to \( 4^{-4} \):
\[ 4^{-4} = \frac{1}{4^4} \]
Next, we need to calculate \( 4^4 \):
\[ 4^4 = 4 \times 4 \times 4 \times 4 \] Calculating step by step:
- \( 4 \times 4 = 16 \)
- \( 16 \times 4 = 64 \)
- \( 64 \times 4 = 256 \)
Thus, \( 4^4 = 256 \), and now substituting back, we have:
\[ 4^{-4} = \frac{1}{256} \]
Therefore, the final answer is:
\[ \boxed{\frac{1}{256}} \]