What is the units digit of 2222^(333)*3333^(444)?	Options:
A) 0
B) 2
C) 4
D) 6
E) 8
Each of the other explanations to this question has properly explained that you need to break down the calculation into pieces and figure out the repeatingpatternof the units digits.   Here's another way to organize the information.   We're given [(2222)^333][(3333)^222]   We can 'combine' some of the pieces and rewrite this product as....   ([(2222)(3333)]^222) [(2222)^111]   (2222)(3333) = a big number that ends in a 6   Taking a number that ends in a 6 and raising it to a power creates a nice pattern:   6^1 = 6   6^2 = 36   6^3 = 216   Etc.   Thus, we know that ([(2222)(3333)]^222) will be a gigantic number that ends in a 6.   2^111 requires us to figure out thecycleof the units digit...   2^1 = 2   2^2 = 4   2^3 = 8   2^4 = 16   2^5 = 32   2^6 = 64   2^7 = 128   2^8 = 256   So, every 4powers, the pattern of the units digits repeats (2, 4, 8, 6.....2, 4, 8, 6....).   111 = 27 sets of 4 with a remainder of 3....   This means that 2^111 = a big number that ends in an 8   So we have to multiply a big number that ends in a 6 and a big number that ends in an 8.   (6)(8) = 48, so the final product will be a gigantic number that ends in an 4.   Final Answer:   4
<result>C</result>
What is the units digit of 2222^(333)*3333^(444)?