Simplify (x^2y^-3)/(x^-1y)

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

Move $y^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Multiply $y$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

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

Multiply $y^{3}$ by $y$ .

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

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

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

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

Add $3$ and $1$ .

$\frac{x^{2}}{x^{- 1} y^{4}}$

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

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

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

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

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

$\frac{x^{2} x^{1}}{y^{4}}$

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

$\frac{x^{2 + 1}}{y^{4}}$

Add $2$ and $1$ .

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