What last number of 18^1000?

The last digit will simply be equal to 8^1000, since the 10 will not have any effect on the units digit. Take the first few powers of 8, examining only the last digit:

8^1=8

8^2=4

8^3=2

8^4=6

8^5=8

8^6=4

We see that it continues in this pattern. Powers evenly divisible by 4, therefore, end in 6. Since 1000 is divisible by 4, 8^1000 ends in 6, so 18^1000 also ends in 6.