Simplify (-10xy^2)(-2x^4y)^3

$(- 10 x y^{2}) {(- 2 x^{4} y)}^{3}$

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

Apply the product rule to $- 2 x^{4} y$ .

$- 10 x y^{2} ({(- 2 x^{4})}^{3} y^{3})$

Apply the product rule to $- 2 x^{4}$ .

$- 10 x y^{2} ({(- 2)}^{3} {(x^{4})}^{3} y^{3})$

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

Move $y^{3}$ .

$- 10 x (y^{3} y^{2}) ({(- 2)}^{3} {(x^{4})}^{3})$

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

$- 10 x y^{3 + 2} ({(- 2)}^{3} {(x^{4})}^{3})$

Add $3$ and $2$ .

$- 10 x y^{5} ({(- 2)}^{3} {(x^{4})}^{3})$

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

$- 10 x y^{5} (- 8 {(x^{4})}^{3})$

Multiply the exponents in ${(x^{4})}^{3}$ .

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

$- 10 x y^{5} (- 8 x^{4 \cdot 3})$

Multiply $4$ by $3$ .

$- 10 x y^{5} (- 8 x^{12})$

Multiply $x$ by $x^{12}$ by adding the exponents.

Move $x^{12}$ .

$- 10 (x^{12} x) y^{5} \cdot - 8$

Multiply $x^{12}$ by $x$ .

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

$- 10 (x^{12} x^{1}) y^{5} \cdot - 8$

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

$- 10 x^{12 + 1} y^{5} \cdot - 8$

Add $12$ and $1$ .

$- 10 x^{13} y^{5} \cdot - 8$

Multiply $- 8$ by $- 10$ .

$80 x^{13} y^{5}$