What is the last digit of $2003^{2003}$? 
What is the last digit of this number?
$$2003^{2003}$$

Thanks in advance.
I don't have any kind of idea how to solve this. Except that $3^3$ is $27$.

$$2003^{2003} = (200*10+3)^{2003}$$ 
Throwing out every term that doesn't influence the last digit
$$=3^{2003} = 3^3 \cdot (3^4)^{500} = 3^3 \cdot (8*10+1)^{500}$$
Again throwing out every term that doesn't influence the last digit
$$=3^3 \cdot (1)^{500}= 3^3 = 2*10+7 $$
Last time throwing out every term that doesn't influence the last digit
$$= 7$$
