Simplify (-4m^2n^3)(2mn)

$(- 4 m^{2} n^{3}) (2 m n)$

Step 1

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

Move $m$ .

$- 4 (m \cdot m^{2}) n^{3} (2 n)$

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

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

$- 4 (m^{1} m^{2}) n^{3} (2 n)$

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

$- 4 m^{1 + 2} n^{3} (2 n)$

Add $1$ and $2$ .

$- 4 m^{3} n^{3} (2 n)$

Step 2

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

Move $n$ .

$- 4 m^{3} (n \cdot n^{3}) \cdot 2$

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

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

$- 4 m^{3} (n^{1} n^{3}) \cdot 2$

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

$- 4 m^{3} n^{1 + 3} \cdot 2$

Add $1$ and $3$ .

$- 4 m^{3} n^{4} \cdot 2$

Step 3

Multiply $2$ by $- 4$ .

$- 8 m^{3} n^{4}$