Simplify ((4x)^(3y))^2: Working with Double Exponents

$((4x)^{3y})^2=$

We'll use the power rule for powers:

$(a^m)^n=a^{m\cdot n}$We'll apply this rule to the expression in the problem:

$((4x)^{3y})^2= (4x)^{3y\cdot2}=(4x)^{6y}$When in the first stage we applied the mentioned power rule and eliminated the outer parentheses, in the next stage we simplified the resulting expression,

Next, we'll recall the power rule for powers that applies to parentheses containing a product of terms:

$(a\cdot b)^n=a^n\cdot b^n$We'll apply this rule to the expression we got in the last stage:

$(4x)^{6y} =4^{6y}\cdot x^{6y}$When we applied the power to the parentheses to each term of the product inside the parentheses.

Therefore, the correct answer is answer D.