Simplify (-2x^2y)^2*(-3xy^3)

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

Step 1

Rewrite using the commutative property of multiplication.

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

Step 2

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

Apply the product rule to $- 2 x^{2} y$ .

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

Apply the product rule to $- 2 x^{2}$ .

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

Step 3

Multiply $y^{2}$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

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

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

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

Add $3$ and $2$ .

$- 3 ({(- 2)}^{2} {(x^{2})}^{2} y^{5}) x$

Step 4

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

$- 3 (4 {(x^{2})}^{2} y^{5}) x$

Step 5

Multiply the exponents in ${(x^{2})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- 3 (4 x^{2 \cdot 2} y^{5}) x$

Multiply $2$ by $2$ .

$- 3 (4 x^{4} y^{5}) x$

Step 6

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

Move $x$ .

$- 3 (4 (x \cdot x^{4}) y^{5})$

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

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

$- 3 (4 (x^{1} x^{4}) y^{5})$

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

$- 3 (4 x^{1 + 4} y^{5})$

Add $1$ and $4$ .

$- 3 (4 x^{5} y^{5})$

Step 7

Multiply $4$ by $- 3$ .

$- 12 x^{5} y^{5}$