To find the units digit for a big group of numbers you have to find a pattern. For example, let's consider the following powers
If we develop some of these powers, we get that the first power has 7 units digit, the second power has 3 unit digits, the third powers has 7, the fourth powers has 3, and so on... In this case, the pattern of unit digits is 7-3-7. So, it would be enough to combine this pattern to get the units digit of the whole.