Simplify ((x^-2)y^4)/(y^-5)

$\frac{(x^{- 2}) y^{4}}{y^{- 5}}$

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

$\frac{y^{4}}{y^{- 5} x^{2}}$

Move $y^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{y^{4} y^{5}}{x^{2}}$

Multiply $y^{4}$ by $y^{5}$ by adding the exponents.

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

$\frac{y^{4 + 5}}{x^{2}}$

Add $4$ and $5$ .

$\frac{y^{9}}{x^{2}}$