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Which is the greatest among (3)^(198), ...

Which is the greatest among `(3)^(198), (27)^(64), (9)^(100)` and `(81)^(49)` ?

A

`(9)^(100)`

B

`(81)^(49)`

C

`(27)^(64)`

D

`3^(198)`

Text Solution

Verified by Experts

The correct Answer is:
A
`3^(198), (27)^(64), (9)^(100), (81)^(49)`
Converting all the numbers with base 3.
`27^(64)=(3^(3))^(64)=3^(192)`
`(9)^(100)=(3^(3))^(100)=3^(200)`
`(81)^(49)=(3^(4))^(49)=3^(196)`
`3^(200)` is the greatest.
`:. 9^(100)` is the geatest.
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