Newtons Inverse Roots?

Algebra Level 5

If $r_1, r_2, r_3, r_4, r_5$ are the complex roots of the equation $x^5-3x^4-1=0$ . Find the value of $\frac{1}{r_1^9}+\frac{1}{r_2^9}+\frac{1}{r_3^9}+\frac{1}{r_4^9}+\frac{1}{r_5^9}.$

Inspiration