What is the simplified form of the expression (4y^4)^3?

To simplify the expression (4y^4)^3, we start by applying the power of a product property, which states that (ab)^n = a^n * b^n. Here, we have a coefficient (4) and a variable term (y^4).

First, we raise the coefficient 4 to the power of 3:

4^3 = 4 * 4 * 4 = 64.

Next, we raise the variable term (y^4) to the power of 3. According to the power of a power property, (x^m)^n = x^(m*n):

(y^4)^3 = y^(4*3) = y^12.

Now, we combine the results:

(4y^4)^3 = 64 * y^12.

Thus, the fully simplified form of the expression is 64y^12. This confirms that the answer provided is indeed the correct choice, as it follows the properties of exponents properly.