Simplify the expression.

[(4^2)^2]^2

work the parentheses from the inside out

or use exponent laws ... 4^8

[(4^2)^2]^2 = [4^4]^2 = 4^8.

To simplify the expression [(4^2)^2]^2, we will work from the inside out.

First, let's simplify the exponent of 4^2:
4^2 = 4 * 4 = 16

Now, we substitute the simplified value back into the expression:
[(4^2)^2]^2 = [(16)^2]^2

Next, let's simplify the exponent of (16)^2:
(16)^2 = 16 * 16 = 256

Now, we substitute the simplified value back into the expression:
[(16)^2]^2 = (256)^2

Finally, let's simplify the exponent of (256)^2:
(256)^2 = 256 * 256 = 65,536

Therefore, the simplified expression is 65,536.