Quandaries
and Queries 

Who is asking: Student Level: Middle Question: Thank you 

Hi Elizabeth, The first step in this problem is to put you calculator away and not use it. Now calculate some powers of 4.
Notice that each time you only need to know the units digit of the previuos power to find the units digit of the next power. For example when multiplying 256 4 you first find 6 4 = 24 and then the rest of the multiplication is not important. The units digit of 256 4 is 4. If the units digit of a power of 4 is 6 then the units digit of the next power of 4 is 4. If the units digit of a power of 4 is 4 then the units digit of the next power of 4 is 6. Thus the units digits form a repeating cycle, 4,6,4,6,4,6,4,6,... So what is the units digit of 4^{478}? Now can you find the units digit of 3^{478}? Penny 

