SOLUTION: What is the last digit of 7^2009 ? A. 1 B. 3 C. 5 D. 7 E. 9

So the last digits go in blocks of 4 like this:  7,9,3,1
 
So we just divide 2009 by 4

   502   
 -----
4)2009
  20
  --
   009
   008
   ---
     1  

That division tells us the last digits go 
through the cycle 7,9,3,1 502 times and the 
remainder, being 1, means that they end up 
on the first of the 503rd cycle and must 
therefore be a 7.

Edwin