1. ## Unit digit

What is the unit digit of the expansion (44)^4,(55)^5,(88)^8..
I want the deep explanation... Please..

2. ## Re: Unit digit

Well one way to do this problem is using mods... but I prefer this way:
List out the units digits of powers of 4:
4, 6, 4, 6, 4... see the pattern?
For powers of 5, the units digit is always 5
For powers of 8, we have the pattern 8, 4, 2, 6, 8, 4, 2, 6, 8...

Another way to do this is to simple do the arithmetic! $44^2= 1936$, $44^3= 85184$, and $44^4= 3748096$.
$55^5= 503284375$, $88^8=3596345248055296$. Nothing "deep" about that!