Simplify ((3m^2n^3)/(xy^2))((x^3yz^2)/(2mn^2))

$(\frac{3 m^{2} n^{3}}{x y^{2}}) (\frac{x^{3} y z^{2}}{2 m n^{2}})$

Combine.

$\frac{3 m^{2} n^{3} (x^{3} y z^{2})}{x y^{2} (2 m n^{2})}$

Cancel the common factor of $m^{2}$ and $m$ .

Factor $m$ out of $3 m^{2} n^{3} (x^{3} y z^{2})$ .

$\frac{m (3 m n^{3} (x^{3} y z^{2}))}{x y^{2} (2 m n^{2})}$

Cancel the common factors.

Factor $m$ out of $x y^{2} (2 m n^{2})$ .

$\frac{m (3 m n^{3} (x^{3} y z^{2}))}{m (x y^{2} (2 n^{2}))}$

Cancel the common factor.

$\frac{m (3 m n^{3} (x^{3} y z^{2}))}{m (x y^{2} (2 n^{2}))}$

Rewrite the expression.

$\frac{3 m n^{3} (x^{3} y z^{2})}{x y^{2} (2 n^{2})}$

Cancel the common factor of $n^{3}$ and $n^{2}$ .

Factor $n^{2}$ out of $3 m n^{3} (x^{3} y z^{2})$ .

$\frac{n^{2} (3 m n (x^{3} y z^{2}))}{x y^{2} (2 n^{2})}$

Cancel the common factors.

Factor $n^{2}$ out of $x y^{2} (2 n^{2})$ .

$\frac{n^{2} (3 m n (x^{3} y z^{2}))}{n^{2} (x y^{2} \cdot (2))}$

Cancel the common factor.

$\frac{n^{2} (3 m n (x^{3} y z^{2}))}{n^{2} (x y^{2} \cdot (2))}$

Rewrite the expression.

$\frac{3 m n (x^{3} y z^{2})}{x y^{2} \cdot (2)}$

Cancel the common factor of $x^{3}$ and $x$ .

Factor $x$ out of $3 m n (x^{3} y z^{2})$ .

$\frac{x (3 m n (x^{2} y z^{2}))}{x y^{2} \cdot (2)}$

Cancel the common factors.

Factor $x$ out of $x y^{2} \cdot (2)$ .

$\frac{x (3 m n (x^{2} y z^{2}))}{x (y^{2} \cdot (2))}$

Cancel the common factor.

$\frac{x (3 m n (x^{2} y z^{2}))}{x (y^{2} \cdot (2))}$

Rewrite the expression.

$\frac{3 m n (x^{2} y z^{2})}{y^{2} \cdot (2)}$

Cancel the common factor of $y$ and $y^{2}$ .

Factor $y$ out of $3 m n (x^{2} y z^{2})$ .

$\frac{y (3 m n (x^{2} z^{2}))}{y^{2} \cdot (2)}$

Cancel the common factors.

Factor $y$ out of $y^{2} \cdot (2)$ .

$\frac{y (3 m n (x^{2} z^{2}))}{y (y \cdot 2)}$

Cancel the common factor.

$\frac{y (3 m n (x^{2} z^{2}))}{y (y \cdot 2)}$

Rewrite the expression.

$\frac{3 m n (x^{2} z^{2})}{y \cdot 2}$

Move $2$ to the left of $y$ .

$\frac{3 m n x^{2} z^{2}}{2 y}$