Evaluate (x^-2y^-4)/(xy^-6)

$\frac{x^{- 2} y^{- 4}}{x y^{- 6}}$

Step 1

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

$\frac{y^{- 4}}{x y^{- 6} x^{2}}$

Step 2

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

Move $x^{2}$ .

$\frac{y^{- 4}}{x^{2} x y^{- 6}}$

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

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

$\frac{y^{- 4}}{x^{2} x^{1} y^{- 6}}$

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

$\frac{y^{- 4}}{x^{2 + 1} y^{- 6}}$

Add $2$ and $1$ .

$\frac{y^{- 4}}{x^{3} y^{- 6}}$

Step 3

Move $y^{- 6}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{y^{- 4} y^{6}}{x^{3}}$

Step 4

Multiply $y^{- 4}$ by $y^{6}$ by adding the exponents.

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

$\frac{y^{- 4 + 6}}{x^{3}}$

Add $- 4$ and $6$ .

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