what is the result of 10^2.

Assuming you are working in decimal, first convert to binary (it is easier to read XOR in binary, normally you would work in hex for compactnes).

10 Dec = 1010 Binary
02 Dec = 0010 Binary

Exclusive OR (or XOR for short) gives a One when the bit in that position is a one on either of the inputs, and a zero on the other. In cases where the input bit is the same, XOR always gives a zero.

Input1 Input2 Output
  0      0       0
  0      1       1
  1      0       1
  1      1       0

So if you XOR 10(dec) with 2(dec) you get 8(dec):

         Dec  Bin 
Input1   10   1010
Input2   02   0010
Output   08   1000