what is the last digit of (2^2^2007)+1

Note:

(2^2^2007) + 1  can be expressed as :

4^(2007) + 1

And the ending digit for all even, positive powers of 4 = 6

And the ending digit for all odd, positive powers of 4 = 4

So.......

(2 ^ 2 ^ 2007)  + 1   = (4^2007) + 1     and since this power of 4 is odd, it ends in a 4....and adding 1 to 4  = 5

Here are the last 10 digits of your number, so you can see what the last digit is:8994576385.