What are roots of higher power like $n^9=512$? We know a value of $n$ in $n^2 = 4$ is $\pm2$ (two roots), then what about $n^9 = 512$, generic answer is $+2$, but it should have $9$ roots. What are those $8$ other roots and how can we find them ?

$$n^9-a^9=(n^3)^3-(a^3)^3=(n^3-a^3)(n^6+a^3n^3+a^6)=(n-a)(n^2+an+a^2)(n^6+a^3n^3+a^6)$$
