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Find the last three digits of the number `27^(27)dot`

Text Solution

Verified by Experts

The correct Answer is:
Last three digits are 803
`27^(27) = 3(10-1)^(40)`
`= 3(10^(40) - .^(40)C_(1) .10^(39) +"….." + .^(40)C_(38).10^(2)-.^(40)C_(39).10+1)`
`= (1000 lambda - 400 + 1)`
`= 3(1000 lambda - 399)`
Therefore, last 3 digits of this number of `803`.
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