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

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

Step 1

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

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

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

Apply the product rule to $- 2 x$ .

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

Step 2

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

Move $x^{3}$ .

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

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

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

Add $3$ and $2$ .

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

Step 3

Rewrite using the commutative property of multiplication.

$- 1 \cdot {(- 2)}^{3} x^{5} {(y^{2})}^{3}$

Step 4

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

$- 1 \cdot - 8 x^{5} {(y^{2})}^{3}$

Step 5

Multiply $- 1$ by $- 8$ .

$8 x^{5} {(y^{2})}^{3}$

Step 6

Multiply the exponents in ${(y^{2})}^{3}$ .

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

$8 x^{5} y^{2 \cdot 3}$

Multiply $2$ by $3$ .

$8 x^{5} y^{6}$