Simplify (6x^3y)(2xz^2)

$(6 x^{3} y) (2 x z^{2})$

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

Move $x$ .

$6 (x \cdot x^{3}) y (2 z^{2})$

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

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

$6 (x^{1} x^{3}) y (2 z^{2})$

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

$6 x^{1 + 3} y (2 z^{2})$

Add $1$ and $3$ .

$6 x^{4} y (2 z^{2})$

Multiply $2$ by $6$ .

$12 x^{4} y z^{2}$