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

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

Step 1

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

Apply the product rule to $- 3 x y$ .

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

Apply the product rule to $- 3 x$ .

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

Step 2

Multiply $- 3$ by ${(- 3)}^{2}$ by adding the exponents.

Move ${(- 3)}^{2}$ .

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

Multiply ${(- 3)}^{2}$ by $- 3$ .

Raise $- 3$ to the power of $1$ .

${(- 3)}^{2} \cdot {(- 3)}^{1} x^{2} y^{2} (x^{2} y^{2})$

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

${(- 3)}^{2 + 1} x^{2} y^{2} (x^{2} y^{2})$

Add $2$ and $1$ .

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

Step 3

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Step 4

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

Move $y^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Step 5

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

$- 27 x^{4} y^{4}$