If n = (33)^43 + (43)^32 what is the units digit of n?
Select the correct option:
A) 0  B) 2  C) 4  D) 6  E) 8
First of all, the units digit of (33)^43 is the same as that of 3^43 and the units digit of (43)^32 is the same as that of 3^32. So, we need to find the units digit of 3^43 + 3^33.   Next, the units digit of 3 in positive integer power repeats in blocks of four {3, 9, 7, 1}:   3^1=3 (the units digit is 3)   3^2=9 (the units digit is 9)   3^3=27 (the units digit is 7)   3^4=81 (the units digit is 1)   3^5=243 (the units digit is 3 again!)   ...   Thus:   The units digit of 3^43 is the same as the units digit of 3^3, so 7 (43 divided by the cyclicity of 4 gives the remainder of 3).   The units digit of 3^33 is the same as the units digit of 3^1, so 3 (33 divided by the cyclicity of 4 gives the remainder of 1).   Therefore the units digit of (33)^43 + (43)^32 is 7 + 5 = 2.   Answer: 2.
<result>B</result>
If n = (33)^43 + (43)^32 what is the units digit of n?