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Using binomial theorem, evaluate : (99)^...

Using binomial theorem, evaluate : `(99)^5`

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The correct Answer is:
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`(99)^(5)=(100-1)^(5)`
`=underset(r=0)overset(5)(Sigma).^(5)C_(r)(100)^(5-r)(-1)^(r)`
`=^(5)C_(0)(100)^(5)(-1)^(0)+^(5)C_(1)(100)^(4)(-1)^(1)`
`+^(5)C_(2)(100)^(3)(-1)^(2)+^(5)C_(3)(100)^(2)(-1)^(3)`
`+^(5)C_(4)(100)^(1)(-1)^(4)+^(5)(100)^(0)(-1)^(5)`
`=1000000000-50000000+10000000`
`-100000+500-1`
`=10010000500-500100001`
`=9509900499`
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