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

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

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

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

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

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

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

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

Factor $y$ out of $y^{1}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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