To solve \((4^2)^3\), you can use the exponentiation rule that states \((a^m)^n = a^{m \cdot n}\).
Here, \(a = 4\), \(m = 2\), and \(n = 3\). Applying the rule:
\[ (4^2)^3 = 4^{2 \cdot 3} = 4^6 \]
Next, calculate \(4^6\):
\[ 4^6 = (2^2)^6 = 2^{2 \cdot 6} = 2^{12} \]
Now calculate \(2^{12}\):
\[ 2^{12} = 4096 \]
Therefore, \((4^2)^3 = 4096\).