Expand what they mean.
(-x)^{8} = (-x)(-x)(-x)(-x)(-x)(-x)(-x)(-x)
and
(-x)^{3} = (-x)(-x)(-x)
And if you want - so you can clear all confusion - prove the general case:
(-x)^{2k} = x, \; k \in \mathbb{Z}
(that is, -x to an even power)
and
(-x)^{2k+1} = -x, \; k \in \mathbb{Z}
(that...