Simplify 3gh^2*4g^3h^3

$3 g h^{2} \cdot 4 g^{3} h^{3}$

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

Move $g^{3}$ .

$3 (g^{3} g) h^{2} \cdot (4 h^{3})$

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

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

$3 (g^{3} g^{1}) h^{2} \cdot (4 h^{3})$

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

$3 g^{3 + 1} h^{2} \cdot (4 h^{3})$

Add $3$ and $1$ .

$3 g^{4} h^{2} \cdot (4 h^{3})$

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

Move $h^{3}$ .

$3 g^{4} (h^{3} h^{2}) \cdot 4$

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

$3 g^{4} h^{3 + 2} \cdot 4$

Add $3$ and $2$ .

$3 g^{4} h^{5} \cdot 4$

Multiply $4$ by $3$ .

$12 g^{4} h^{5}$