Simplify (x^-1y)/(xy^-2)

$\frac{x^{- 1} y}{x y^{- 2}}$

Move $x^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{y}{x y^{- 2} x}$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$\frac{y}{x \cdot x y^{- 2}}$

Multiply $x$ by $x$ .

$\frac{y}{x^{2} y^{- 2}}$

Move $y^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

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

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

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

$\frac{y^{1} y^{2}}{x^{2}}$

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

$\frac{y^{1 + 2}}{x^{2}}$

Add $1$ and $2$ .

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