Simplify (2mn^2)(5m^2n)

$(2 m n^{2}) (5 m^{2} n)$

Step 1

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

Move $m^{2}$ .

$2 (m^{2} m) n^{2} (5 n)$

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

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

$2 (m^{2} m^{1}) n^{2} (5 n)$

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

$2 m^{2 + 1} n^{2} (5 n)$

Add $2$ and $1$ .

$2 m^{3} n^{2} (5 n)$

Step 2

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

Move $n$ .

$2 m^{3} (n \cdot n^{2}) \cdot 5$

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

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

$2 m^{3} (n^{1} n^{2}) \cdot 5$

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

$2 m^{3} n^{1 + 2} \cdot 5$

Add $1$ and $2$ .

$2 m^{3} n^{3} \cdot 5$

Step 3

Multiply $5$ by $2$ .

$10 m^{3} n^{3}$