What is the unit digit of the expansion (44)^4,(55)^5,(88)^8..

I want the deep explanation... Please..(Crying)

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- Oct 22nd 2012, 04:56 AMkohilaUnit digit
What is the unit digit of the expansion (44)^4,(55)^5,(88)^8..

I want the deep explanation... Please..(Crying) - Oct 28th 2012, 08:31 AMMrdavid445Re: 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...

You can use this to help find your answer - Oct 29th 2012, 02:15 PMHallsofIvyRe: Unit digit
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!