If n = (33)^43 + (23)^33 what is the units digit of n?	Pick.
A) 0	B) 2	C) 4	D) 6	E) 8
First of all, the units digit of (33)^23 is the same as that of 3^23 and the units digit of (23)^33 is the same as that of 3^33. So, we need to find the units digit of 3^23 + 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 3^23 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)^23 + (23)^33 is  3 + 3= 
<gadget id="calculator"> 3 + 3</gadget>
<output>6</output>
6.   Answer: 6.
<result>D</result>
If n = (33)^43 + (23)^33 what is the units digit of n?