I really am not sure how to make headway on this exercise.
And what do I have wrong with $(-1)^{n_1-n_2+n_3} = (-1)^{n_1}(-1)^{n_2}(-1)^{n_3} = (-1)^n$? Because from there I would have the statement as equivalent to $(-1 + -1 + -1)^n$, which clearly isn't right.