Find the Product (2xy)^2(-3x^2)(4y^2)

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

Rewrite using the commutative property of multiplication.

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

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $2 x y$ .

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

Apply the product rule to $2 x$ .

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

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

Move $x^{2}$ .

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

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

$- 3 (2^{2} x^{2 + 2} y^{2}) (4 y^{2})$

Add $2$ and $2$ .

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

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

Move $y^{2}$ .

$- 3 (2^{2} x^{4} (y^{2} y^{2})) \cdot 4$

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

$- 3 (2^{2} x^{4} y^{2 + 2}) \cdot 4$

Add $2$ and $2$ .

$- 3 (2^{2} x^{4} y^{4}) \cdot 4$

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

$- 3 (4 x^{4} y^{4}) \cdot 4$

Multiply $4$ by $- 3$ .

$- 12 (x^{4} y^{4}) \cdot 4$

Multiply $4$ by $- 12$ .

$- 48 x^{4} y^{4}$