Question

how do you simplify (-1)^2099?

Answer 1

just think about what \[-1^2, -1^3, -1^4, -1^5, -1^6, -1^7\] is..
See any regularity? About odd and even exponent maybe?
Try to come up with a rule and then plug in 2099...

Answer 2

1 to any power is still 1. In this particular case you have a -1. Therefore, the sign is what will change. A (-1) to an even power will make 1 positive, and a (-1) to an odd power will make 1 a negative. Since the power is 2099 which is odd, the sign will be a negative and you will get: -1