Problem:
What is the units digit of .
Answer Choices:
A.
B.
C.
D.
E.
Solution:
To determine the units digit of , looking for patterns is a good approach to finding the solution. The units digit of each power of depends only on the units digit of the previous power, as follows:
For , the units digit is .
For , so the units digit is .
For , so the units digits is .
For , so the units digit is .
For , so the units digit is .
The units digits of successive powers of follow the pattern ,
Since , the units digit of is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions