Question 439889
<pre>
(-1)<sup>2099</sup> = (-1)<sup>1</sup>(-1)<sup>2098</sup> = 
(-1)(-1)<sup>2*1049</sup> = (-1)[(-1)<sup>2</sup>]<sup>1049</sup> =
(-1)(1)<sup>1049</sup> = (-1)(1) = -1

Or, you can just learn the two rules about -1:

(-1)<sup>EVEN</sup> = 1
(-1)<sup>ODD</sup> = -1

and since 2099 is odd, the answer is -1. 

Edwin</pre>