Question

Find a indicated real nth root(s)a.
n=9, a=-512

The root is = ?

Answer 1

We know that 512=2^9, which implies that (-2)^9=-512 (since 9 is odd).  Thus -2 is one of the 9th root of -512.

There are 8 (or 4 pairs of) other roots that are excluded because they are complex.

Therefore -2 is the only real 9th root of -512.