Divide (x^-1y^2)/(x^2y^-1)

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

Step 1

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

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

Step 2

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

$\frac{y^{2}}{x^{3} y^{- 1}}$

Step 3

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

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

Step 4

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

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

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

$\frac{y^{2} y^{1}}{x^{3}}$

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

$\frac{y^{2 + 1}}{x^{3}}$

Add $2$ and $1$ .

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