Which number below is the greatest?

(a) `6^100`

(b) `5^200`

(c) `4^300`

(d) `3^400`

(e) `2^500`

### 1 Answer | Add Yours

Let us make a common indice for all numbers.

`6^100=6^100`

`5^200 = 5^(2 xx 100) = (5^2)^100=25^100`

`4^300=(4^3)^100=64^100`

`3^400=(3^4)^100=81^100`

`2^500=(2^5)^100=32^100`

Since the indices are common for all numbers we can easily say the largest number is 81^100.

*So the largest number is `3^400`. The correct answer is at option (d)*

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