To simplify the expression \( \left(2^{-3}\right)^4 \), you can use the property of exponents that states \( (a^m)^n = a^{m \cdot n} \).
Applying this property:
\[ \left(2^{-3}\right)^4 = 2^{-3 \cdot 4} = 2^{-12} \]
Thus, \( \left(2^{-3}\right)^4 \) is equivalent to \( 2^{-12} \).
If you want to express this in a different form, you can also write:
\[ 2^{-12} = \frac{1}{2^{12}} \]
Therefore, the final answer is:
\[ 2^{-12} \quad \text{or} \quad \frac{1}{2^{12}} \]