Explanation

In this question, one idea is to attempt to harmonize these terms into a single exponent, such as by finding a common base. But 103 is not divisible by 3. Another approach is to try to figure out the units digit of each term individually and then see what they must sum to. Evidently they will reliably sum to a particular digit, since the question has a particular answer.

We can look at cases of powers of 3:

1: 3

2: 9

3: 27

4: 81

5: 243

6:

We can speculate, then confirm by imagining further multiplication, that we have a repeating sequence, since got back to a final digit of 3, which yields 9, as before, which will yield 7, as before, and so on. There are four different possible digits: 3, 9, 7, and 1. For this high powers, we need to count and figure out which one each lands on. In the second term, the 95th power goes through the cycle times. Namely, times goes through 3, 9, 7, 1 an even number of times. Then we have 93, 94, and 95, which lands us on 7. The first term, by similar logic, lands us on a 7. So the sum of these two numbers will involve adding two units digits of 7, which will result in a units digit of 4.

The correct answer is (E).