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Write last two digits of the number 3^(4...

Write last two digits of the number `3^(400)dot`

Text Solution

Verified by Experts

The correct Answer is:
1
Given that, `3^(400) = g^(200) = (10 - 1)^(200)`
`rArr (10 - 1)^(200) = .^(200)C_(n) 10^(200) - .^(200)C_(1) 10^(199) + .... - .^(200)C_(199) 10^(1) + .^(200)C_(200) 1^(200)`
`rArr (10 - 1)^(200) = 10^(200) - 200 xx 10^(199) + ...... - 10 xx 200 + 1`
So, it is clear that the last two digits are 01.
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