13^655: Find the last digit of a number raised to a large power

Find the last digit when 13 is raised to 655.

131=13

132=169

133=2,197

134=28,561

135=371,293

136=4,826,809

137=62,748,517

138=815,730,721

139=10,604,499,373

1310=137,858,491,849

1311=1,792,160,394,037

1312=23,298,085,122,481
 

Notice the last digit of the number in each row is making the following pattern
3, 9, 7, 1, 3, 9, 7, 1, 3, 9, 7, 1

The pattern 3, 9, 7, 1 repeats every four rows. Now count how many times this pattern will repeat in 655 rows. To do that, simply count how many 4-rows are there in 655.
655÷4=163 remainder 3

This simply means that there are 163 counts of full { 3, 9, 7, 1 } and the remainder represents 3 more rows. The three remaining rows in the pattern are { 3, 9, 7 }.

Thus, the last digit of 13655 is 7.