Question

To find the unit digit of number which is in the form a^b. (Ex: 7¹⁰⁵, 9¹²⁵) 

1) If b is not divisible by 4
Step 1: Divide b by 4, if it is not divisible then find the remainder of b when divided by 4. 
Step 2: Units digit = a^r, r is the remainder. 

2) If b is multiple of 4
Units digit is 6: When even numbers 2, 4, 6, 8 are raised to multiple of 4. 
Units digit is 1: When odd numbers 3, 7 and 9 are raised to multiple of 4.