To find \( f(-4) \) for the function \( f(x) = (x^8)^2 \), we first substitute \( -4 \) into the function:
\[ f(-4) = ((-4)^8)^2 \]
Now, we calculate \( (-4)^8 \):
\[ (-4)^8 = 4^8 = (4^4)^2 = 256^2 = 65536 \]
Next, we square that result: \[ f(-4) = (65536)^2 \]
Calculating \( 65536^2 \) results in: \[ 65536^2 = 4294967296 \]
Thus, \[ f(-4) = 4294967296 \]
The final answer is: \[ f(-4) = 4294967296 \]