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# Is a^b > b^a?

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Director
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Is a^b > b^a? [#permalink]  20 May 2013, 22:31
00:00

Difficulty:

45% (medium)

Question Stats:

64% (02:28) correct 36% (01:14) wrong based on 66 sessions
Is a^b > b^a? ( both a and b are non zero integers)

1) a = b^3
2) b < 3

[Reveal] Spoiler: OA

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Math Expert
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Re: Is a^b > b^a? [#permalink]  20 May 2013, 23:50
Expert's post
fozzzy wrote:
Is a^b > b^a? ( both a and b are non zero integers)

1) a = b^3
2) b < 3

Even when combining the statements we can have an YES as well as a NO answer:

If a=-8 and b=-2, then $$a^b=\frac{1}{64}>\frac{1}{256}=b^a$$.
If a=b=1, then a^b = b^a.

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Kudos [?]: 456 [0], given: 543

Re: Is a^b > b^a? [#permalink]  21 May 2013, 00:14
What would be a good way to tackle statement 1

would you substitute in the main equation or use examples?
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Math Expert
Joined: 02 Sep 2009
Posts: 27492
Followers: 4312

Kudos [?]: 42270 [0], given: 6012

Re: Is a^b > b^a? [#permalink]  21 May 2013, 00:20
Expert's post
fozzzy wrote:
What would be a good way to tackle statement 1

would you substitute in the main equation or use examples?

Easy to get answer with number plugging, so I'd stick with this method.
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Re: Is a^b > b^a?   [#permalink] 21 May 2013, 00:20
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