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

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

Step 1

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

Move $u^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Step 2

Multiply $u^{4}$ by $u$ by adding the exponents.

Move $u$ .

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

Multiply $u$ by $u^{4}$ .

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

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

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

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

Add $1$ and $4$ .

$- 3 u^{5} (- 1 v^{2}) (2 v)$

Step 3

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

Move $v$ .

$- 3 u^{5} (- 1 (v \cdot v^{2})) \cdot 2$

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

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

$- 3 u^{5} (- 1 (v^{1} v^{2})) \cdot 2$

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

$- 3 u^{5} (- 1 v^{1 + 2}) \cdot 2$

Add $1$ and $2$ .

$- 3 u^{5} (- 1 v^{3}) \cdot 2$

Step 4

Rewrite using the commutative property of multiplication.

$- 3 \cdot - 1 u^{5} v^{3} \cdot 2$

Step 5

Multiply $- 3$ by $- 1$ .

$3 u^{5} v^{3} \cdot 2$

Step 6

Multiply $2$ by $3$ .

$6 u^{5} v^{3}$