Does "3^3^3" or  mean  or ?


I will assume it's ; otherwise we'd just do it with the calculator
 and the answer would obviously be 3.

So I assume you mean:



30 = 1
31 = 3
32 = 9
33 = 27

34 = 81
35 = 243
36 = 729
37 = 2187

We can see that the last digits repeat in cycles of 4:  1,3,5,7,1,3,5,7,...
So the last digit of  is the same as the last digit of n mod 4.

Therefore since  is the same as , and since 27 mod 4 = 3, 
the last digit of it is the same as the last digit of , so the answer is 7. 

Edwin