Simplify (-u^2)(-6u^2v^3)(-u^3v^4)

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

Step 1

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

Move $u^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Step 2

Multiply $u^{4}$ by $u^{3}$ by adding the exponents.

Move $u^{3}$ .

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

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

$- u^{3 + 4} (- 6 v^{3}) (- 1 v^{4})$

Add $3$ and $4$ .

$- u^{7} (- 6 v^{3}) (- 1 v^{4})$

Step 3

Multiply $v^{3}$ by $v^{4}$ by adding the exponents.

Move $v^{4}$ .

$- u^{7} (- 6 (v^{4} v^{3})) \cdot - 1$

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

$- u^{7} (- 6 v^{4 + 3}) \cdot - 1$

Add $4$ and $3$ .

$- u^{7} (- 6 v^{7}) \cdot - 1$

Step 4

Rewrite using the commutative property of multiplication.

$- 1 \cdot - 6 u^{7} v^{7} \cdot - 1$

Step 5

Multiply $- 1$ by $- 6$ .

$6 u^{7} v^{7} \cdot - 1$

Step 6

Multiply $- 1$ by $6$ .

$- 6 u^{7} v^{7}$