Simplify (-2u)(u^2v)(4u^3v^3)

$(- 2 u) (u^{2} v) (4 u^{3} v^{3})$

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

Move $u^{2}$ .

$- 2 (u^{2} u) v (4 u^{3} v^{3})$

Multiply $u^{2}$ by $u$ .

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

$- 2 (u^{2} u^{1}) v (4 u^{3} v^{3})$

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

$- 2 u^{2 + 1} v (4 u^{3} v^{3})$

Add $2$ and $1$ .

$- 2 u^{3} v (4 u^{3} v^{3})$

Multiply $u^{3}$ by $u^{3}$ by adding the exponents.

Move $u^{3}$ .

$- 2 (u^{3} u^{3}) v (4 v^{3})$

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

$- 2 u^{3 + 3} v (4 v^{3})$

Add $3$ and $3$ .

$- 2 u^{6} v (4 v^{3})$

Multiply $v$ by $v^{3}$ by adding the exponents.

Move $v^{3}$ .

$- 2 u^{6} (v^{3} v) \cdot 4$

Multiply $v^{3}$ by $v$ .

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

$- 2 u^{6} (v^{3} v^{1}) \cdot 4$

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

$- 2 u^{6} v^{3 + 1} \cdot 4$

Add $3$ and $1$ .

$- 2 u^{6} v^{4} \cdot 4$

Multiply $4$ by $- 2$ .

$- 8 u^{6} v^{4}$