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Which number below is the greatest?(a) `6^100` (b) `5^200` (c) `4^300` (d) `3^400` (e)...

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christiano-cr7 | Salutatorian

Posted September 27, 2013 at 8:01 AM via web

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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

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted September 27, 2013 at 8:08 AM (Answer #1)

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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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