Simplify (3xy)(4x^2y^3)

$(3 x y) (4 x^{2} y^{3})$

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

Move $x^{2}$ .

$3 (x^{2} x) y (4 y^{3})$

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

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

$3 (x^{2} x^{1}) y (4 y^{3})$

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

$3 x^{2 + 1} y (4 y^{3})$

Add $2$ and $1$ .

$3 x^{3} y (4 y^{3})$

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

Move $y^{3}$ .

$3 x^{3} (y^{3} y) \cdot 4$

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

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

$3 x^{3} (y^{3} y^{1}) \cdot 4$

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

$3 x^{3} y^{3 + 1} \cdot 4$

Add $3$ and $1$ .

$3 x^{3} y^{4} \cdot 4$

Multiply $4$ by $3$ .

$12 x^{3} y^{4}$