Evaluate (x^2y^-5)/(x^-8y^-8)

$\frac{x^{2} y^{- 5}}{x^{- 8} y^{- 8}}$

Move $x^{- 8}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{x^{2} y^{- 5} x^{8}}{y^{- 8}}$

Move $y^{- 8}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$x^{2} y^{- 5} x^{8} y^{8}$

Multiply $x^{2}$ by $x^{8}$ by adding the exponents.

Move $x^{8}$ .

$x^{8} x^{2} y^{- 5} y^{8}$

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

$x^{8 + 2} y^{- 5} y^{8}$

Add $8$ and $2$ .

$x^{10} y^{- 5} y^{8}$

Multiply $y^{- 5}$ by $y^{8}$ by adding the exponents.

Move $y^{8}$ .

$x^{10} (y^{8} y^{- 5})$

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

$x^{10} y^{8 - 5}$

Subtract $5$ from $8$ .

$x^{10} y^{3}$