Simplify the fraction so there are no negative exponents

Question

Simplify the fraction so there are no negative exponents $$\frac{x^{-9}+y^{-9}}{\frac{x^3+y^3}{y^{-2}}}=\frac AB$$

Tried everything with this problem but cannot get the answer in a quiz that doesn't reveal the right answer but only tells you you are wrong!

Answer 1

HINT

$$x^{-9}+y^{-9}=\frac{x^9+y^9}{x^9y^9}$$

$$x^9+y^9=(x^3+y^3)(x^6-x^3y^3+y^6)$$

Answer 2

Observe that $x^{-9}+y^{-9}=\frac{1}{x^9}+\frac{1}{y^9}=\frac{x^9y^9}{x^9+y^9}$. Also, $\frac{1}{\frac{1}{y^{-2}}}=\frac{1}{y^2}$.