**PROBLEM 1-9-2**

What is the last digit of 2^31921?

(**^** means to the power of...)

2^1 = **2 **

2^2 = **4**

2^3 =** 8**

2^4 = 1**6 **

2^5 = 3**2**

2^6 = 6**4**

2^7 = 12**8**

2^8 = 25**6**

2^9 = 51**2**

2^10 = 102**4**

2^11 = 204**8 **

2^12 = 409**6 **

Looking at the pattern, any odd power ends in 2 or 8.

31921 / 4 = 7980.25 or 7980 and 1/4

1/4 is the group of 4 (looking at the last digit: 2,4,8,6); **therefore, the last digit is a 2. **