Simplify (2x)^2(4y)^2

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

Step 1

Apply the product rule to $2 x$ .

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

Step 2

Raise $2$ to the power of $2$ .

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

Step 3

Apply the product rule to $4 y$ .

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

Step 4

Rewrite using the commutative property of multiplication.

$4 \cdot 4^{2} x^{2} y^{2}$

Step 5

Multiply $4$ by $4^{2}$ by adding the exponents.

Multiply $4$ by $4^{2}$ .

Raise $4$ to the power of $1$ .

$4^{1} \cdot 4^{2} x^{2} y^{2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4^{1 + 2} x^{2} y^{2}$

Add $1$ and $2$ .

$4^{3} x^{2} y^{2}$

Step 6

Raise $4$ to the power of $3$ .

$64 x^{2} y^{2}$