Let's say we have the base -2 and we raise it to the third power, what will happen?
Well, [tex]-2^3 = -2 * -2 * -2[/tex].
[tex]-2 * -2 * -2 = (-2 * -2) * -2 = (4) * -2 = -8[/tex]
Any negative base with an odd exponent will result in a negative answer, because, unlike even exponents and negative bases, the negatives will not cancel out.