Now we have $$\left(\frac{1}{5}\right)^{2000}=\left(\frac{2}{10}\right)^{2000}$$

As we can see the last digit of the decimal representation will be the unit digit of 2^2000. Now the cyclicity of 2 is 4, i.e powers of 2 repeats its unit digit after every 4 units. Now divide 2000 by 4, we get remainder as 0 . So we can say that 2^2000 is equivalent to 2^4. Hence the unit digit of 2^2000 is the unit digit of 2^4. Hence the unit digit is 6