To simplify the expression \(-4^{-4}\), we can apply the properties of exponents.
First, recall that \(a^{-n} = \frac{1}{a^n}\). Therefore, we can rewrite \(-4^{-4}\) as:
\[
-4^{-4} = -\frac{1}{(-4)^4}
\]
Next, we calculate \((-4)^4\):
\[
(-4)^4 = (-4) \times (-4) \times (-4) \times (-4) = 16 \times 16 = 256
\]
Now substitute this back into the expression:
\[
-4^{-4} = -\frac{1}{256}
\]
Thus, the simplified expression is:
\[
-\frac{1}{256}
\]