Help!!!

What is the units digit of 3^1992?

$3^{1992} \pmod {10} = \ ?\\$

$\begin{array}{rcl} 3^{4} \equiv 81 \equiv 1 \pmod {10} \end{array}$

$\begin{array}{rcl} 3^{1992} &\equiv& 3^{4\cdot 498}\pmod {10} \\ &\equiv& (3^{4})^{498}\pmod {10} \qquad 3^{4} \equiv 1 \pmod {10}\\ &\equiv& (1)^{498}\pmod {10}\\ &\equiv& 1 \pmod {10}\\ \mathbf{3^{1992}} & \mathbf{\equiv} & \mathbf{ 1\pmod {10} } \end{array}$

I don't know what you mean by "unit digits"!!. This is very large number with over 950 digits long!. It begins with:2.6640317813178655839963033366326 X 10^950.....and ends with.........9945003411 3558011041.

Thanks Heureka,

I started doing it the same as you but I have not as yet commited this technique to my brain.

so I got a bit lost.  

Thanks so much for reminding me, maybe next time I will answer one like this myself  

 Could you look at this one please and either answer it or comment on it.  That would be great. :)

Thans you :)

web2.0calc.com/questions/f-x-e-x-x-1_2

Thank you so much to everyone who answered! You were all really helpful!  ☺