What is the unit digit of the expansion (44)^4,(55)^5,(88)^8..
I want the deep explanation... Please..
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...
You can use this to help find your answer
Another way to do this is to simple do the arithmetic! $\displaystyle 44^2= 1936$, $\displaystyle 44^3= 85184$, and $\displaystyle 44^4= 3748096$.
$\displaystyle 55^5= 503284375$, $\displaystyle 88^8=3596345248055296$. Nothing "deep" about that!