Simplify (x^-2y)/(x^4y^-1)

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

Step 1

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

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

Step 2

Multiply $x^{4}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

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

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

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

Add $2$ and $4$ .

$\frac{y}{x^{6} y^{- 1}}$

Step 3

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

$\frac{y \cdot y}{x^{6}}$

Step 4

Multiply $y$ by $y$ .

$\frac{y^{2}}{x^{6}}$