You can
put this solution on YOUR website!
(-1)2099 = (-1)1(-1)2098 =
(-1)(-1)2*1049 = (-1)[(-1)2]1049 =
(-1)(1)1049 = (-1)(1) = -1
Or, you can just learn the two rules about -1:
(-1)EVEN = 1
(-1)ODD = -1
and since 2099 is odd, the answer is -1.
Edwin