Simplify 3m^3n^2*8mn^3

$3 m^{3} n^{2} \cdot 8 m n^{3}$

Step 1

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

Move $m$ .

$3 (m \cdot m^{3}) n^{2} \cdot (8 n^{3})$

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

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

$3 (m^{1} m^{3}) n^{2} \cdot (8 n^{3})$

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

$3 m^{1 + 3} n^{2} \cdot (8 n^{3})$

Add $1$ and $3$ .

$3 m^{4} n^{2} \cdot (8 n^{3})$

Step 2

Multiply $n^{2}$ by $n^{3}$ by adding the exponents.

Move $n^{3}$ .

$3 m^{4} (n^{3} n^{2}) \cdot 8$

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

$3 m^{4} n^{3 + 2} \cdot 8$

Add $3$ and $2$ .

$3 m^{4} n^{5} \cdot 8$

Step 3

Multiply $8$ by $3$ .

$24 m^{4} n^{5}$