In the official guide question 183, we are told to use the last digits short-cut to solve the question. We evaluate 3^43 + 3^33 using the short-cut method. The pattern for 3 is given as 3, 9, 7, 1 repeating. Since 40 is a multiple of 4, the units digit of 3^40 = 1. Cutting forward 3 times gives us a...