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.
