Answer
-$3$
Work Step by Step
So we are taking $n$ as the index, while we take $a$ as the number to be under the radical.
Then, we simply check parity and solve,
If the index is even, then we consider both the positive and negative root, but do not find a real root if a is negative.
If the index is odd, then we consider 1 root, which must be of the same sign of $a$.
$-243^{1/5}=-(3^5)^{1/5}=-3^{1}=-3$
