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.

Thanks