at first, i can't understand what you posted.. well, i will edit this for you..

well, the explanation was given to you..

note that the unit digit repeats every after 4 powers..

obeserv also that

1= 4(0)+1

2=4(0)+2

3=4(0)+3

4=4(1)+0

5=4(1)+1

and with powers 1,5,9,... etc, they will have unit digit as 3;

with powers 2,6,10,... etc, they will have unit digit as 9;

with powers 3,7,11,... etc, they will have unit digit as 7;

with powers 4,8,12,... etc, they will have unit digit as 1;

now, 100=4(25)+0.. and notice that the similarity i has with 4=4(1)+0 is the thing you added to the multiple of 4..

why pick 4 and why not pick 5? the unit digits repeat every after 4 powers..

you may compute for .. 99 = 4(24)+ 3.. because of this, the unit digit of is the same as the unit digit of which is 7..