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19 September, 08:28

What last number of 18^1000?

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  1. 19 September, 09:46
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    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.
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