To simplify the expression \( \frac{1}{8^{-4}} \), we can use the property of exponents that states \( a^{-n} = \frac{1}{a^n} \).
Starting with the expression:
\[ \frac{1}{8^{-4}} = 8^{4} \]
Now, we compute \( 8^4 \):
\[ 8^4 = (2^3)^4 = 2^{3 \times 4} = 2^{12} \]
Next, we can calculate \( 2^{12} \):
\[ 2^{12} = 4096 \]
Thus, the simplified expression is:
\[ \frac{1}{8^{-4}} = 4096 \]
The final answer is:
\[ \boxed{4096} \]