Simplify (3x^2y^2)/(2x^-1*(4yx^2))

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

Step 1

Multiply $x^{- 1}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

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

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

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

Subtract $1$ from $2$ .

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

Step 2

Reduce the expression by cancelling the common factors.

Simplify $2 x^{1} \cdot (4 y)$ .

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

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

Factor $x$ out of $3 x^{2} y^{2}$ .

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

Cancel the common factors.

Factor $x$ out of $2 x \cdot (4 y)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

Factor $y$ out of $3 x y^{2}$ .

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

Cancel the common factors.

Factor $y$ out of $2 \cdot (4 y)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Multiply $2$ by $4$ .

$\frac{3 x y}{8}$