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

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

Step 1

Apply the product rule to $- 3 x$ .

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

Step 2

Raise $- 3$ to the power of $2$ .

$9 x^{2} {(- x y)}^{2}$

Step 3

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

Apply the product rule to $- x y$ .

$9 x^{2} ({(- x)}^{2} y^{2})$

Apply the product rule to $- x$ .

$9 x^{2} ({(- 1)}^{2} x^{2} y^{2})$

Step 4

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

Move $x^{2}$ .

$9 (x^{2} x^{2}) ({(- 1)}^{2} y^{2})$

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

$9 x^{2 + 2} ({(- 1)}^{2} y^{2})$

Add $2$ and $2$ .

$9 x^{4} ({(- 1)}^{2} y^{2})$

Step 5

Rewrite using the commutative property of multiplication.

$9 \cdot {(- 1)}^{2} x^{4} y^{2}$

Step 6

Raise $- 1$ to the power of $2$ .

$9 \cdot 1 x^{4} y^{2}$

Step 7

Multiply $9$ by $1$ .

$9 x^{4} y^{2}$