Ok, so my homework was to figure out how negative integers are affected by exponents. The questions were:
-3^2 = __
-3^3 = __
-3^4 = __
-3^5 = __
So I got positive answers for all of these questions. Then I noticed one last problem at the end of my assignment:
In working with powers having a negative base:
--if the exponent is odd, the sign on the answer is ______________.
--if the exponent is even the sign on the answer is ______________.
So my question is: Why does the odd/even thing make a difference as to the sign of the answer? I know what the actual answers to the last questions ARE, thanks to a bit of googling, I just don't understand the hows and whys.