Question

what do you know about the sign of a negative integer raised to an odd power and even power

Answer 1

Look at a number such as -2. Raised to an even power (say 2) is -2*-2 = +4.
Or raised to 4 (another even power) is -2*-2*-2*-2 = +16. Both 4 and 16 are positive numbers.
Raise -2 to an odd power (say 3) and we have -2*-2*-2 = -8 (a negative answer).
Or raised to -5 is
-2*-2*-2*-2*-2 = -32 (a negative answer). You should be able to get the connection from these example.