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

$\frac{3 x y^{2}}{4 y} \cdot \frac{2 x^{2}}{3 y}$

Combine.

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

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

Move $x^{2}$ .

$\frac{3 (x^{2} x) y^{2} \cdot 2}{4 y (3 y)}$

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

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

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

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

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

Add $2$ and $1$ .

$\frac{3 x^{3} y^{2} \cdot 2}{4 y (3 y)}$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$\frac{3 x^{3} y^{2} \cdot 2}{4 (y \cdot y) \cdot 3}$

Multiply $y$ by $y$ .

$\frac{3 x^{3} y^{2} \cdot 2}{4 y^{2} \cdot 3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x^{3} y^{2} \cdot 2}{4 y^{2} \cdot 3}$

Rewrite the expression.

$\frac{x^{3} y^{2} \cdot 2}{4 y^{2}}$

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

Cancel the common factor.

$\frac{x^{3} y^{2} \cdot 2}{4 y^{2}}$

Rewrite the expression.

$\frac{x^{3} \cdot 2}{4}$

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $x^{3} \cdot 2$ .

$\frac{2 \cdot x^{3}}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$\frac{2 \cdot x^{3}}{2 \cdot 2}$

Cancel the common factor.

$\frac{2 \cdot x^{3}}{2 \cdot 2}$

Rewrite the expression.

$\frac{x^{3}}{2}$