To evaluate the expression \( (2^4)^2 \), we can use the property of exponents that states \( (a^m)^n = a^{m \cdot n} \).
Here, we have:
\[ (2^4)^2 = 2^{4 \cdot 2} = 2^8 \]
Next, we calculate \( 2^8 \):
\[ 2^8 = 256 \]
Therefore, the value of the expression \( (2^4)^2 \) is \( 256 \).