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

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

Step 1

Rewrite using the commutative property of multiplication.

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

Step 2

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

Apply the product rule to $- 2 x y$ .

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

Apply the product rule to $- 2 x$ .

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

Step 3

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

Move $x^{2}$ .

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

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

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

Add $2$ and $3$ .

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

Step 4

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

$- (- 8 x^{5} y^{3})$

Step 5

Multiply $- 8$ by $- 1$ .

$8 x^{5} y^{3}$