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# Is a^b > b^a?

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Director
Joined: 29 Nov 2012
Posts: 758

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20 May 2013, 22:31
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Difficulty:

55% (hard)

Question Stats:

68% (02:06) correct 32% (01:53) wrong based on 196 sessions

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Is a^b > b^a? ( both a and b are non zero integers)

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

Math Expert
Joined: 02 Sep 2009
Posts: 52294
Re: Is a^b > b^a?  [#permalink]

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20 May 2013, 23:50
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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Director
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Re: Is a^b > b^a?  [#permalink]

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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?
Math Expert
Joined: 02 Sep 2009
Posts: 52294
Re: Is a^b > b^a?  [#permalink]

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21 May 2013, 00:20
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]

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21 Feb 2017, 01:11
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Re: Is a^b > b^a? &nbs [#permalink] 21 Feb 2017, 01:11
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