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hgp2k
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GMAT Club test M25: # 31 Updated on: 09 Nov 2009, 21:52
Originally posted by hgp2k on 09 Nov 2009, 21:47.
Last edited by hgp2k on 09 Nov 2009, 21:52, edited 1 time in total.
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Guys help me understand one thing here.

Is 3^3^3 = 3^9 or 3^27?
I think it should be 3^9 and not 3^27
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srini123
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GMAT Club test M25: # 31 09 Nov 2009, 21:51
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3^3=27

and 3^3^3 = 3^27

where is the doubt ?
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GMAT Club test M25: # 31 09 Nov 2009, 21:53
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hgp2k
Guys help me understand one thing here.

Is 3^3^3 = 3^9 or 3^27?
I think it should be 3^9 and not 3^27
Show more


It is 3^27

3^3^3 = 3^(3^3) = 3^27
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GMAT Club test M25: # 31 09 Nov 2009, 21:55
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srini123
3^3=27

and 3^3^3 = 3^27

where is the doubt ?
Show more

srini123
I can understand if the question is: 3^(3^3). In this case we have to solve the bracket first. But the question does not say that. So according to basic rules of exponents, it should be 3^(3*3) = 3^9 and not 3^27.
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GMAT Club test M25: # 31 09 Nov 2009, 22:00
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hgp2k
srini123
3^3=27

and 3^3^3 = 3^27

where is the doubt ?

srini123
I can understand if the question is: 3^(3^3). In this case we have to solve the bracket first. But the question does not say that. So according to basic rules of exponents, it should be 3^(3*3) = 3^9 and not 3^27.
Show more
- also I didn't quite get where did the * come from ? I see now, \(((3^3)^3 = 3^9)\), but for the one in question we need to apply precedence of operators (see below)

As per precedence of power, 3^3^3 = 3^(3^3)

see https://en.wikipedia.org/wiki/Order_of_operations
specifically, example
2. Evaluate exponential powers; for iterated powers, start from the right:

2^{3^2}=2^{[3^2]}=[2^9]=512
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GMAT Club test M25: # 31 09 Nov 2009, 22:08
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okay, I got it now. Thanks Srini +1 for quick answer and all your help :)
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GMAT Club test M25: # 31 10 Nov 2009, 00:48
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This question has already been discussed:
gmat-test-m25-master-thread-all-discussions-78460.html

Please don't create double posts on the same questions. You can search this thread:
gmat-club-tests-master-threads-all-tests-78599.html

Also, don't forget to use forum search and Custom Google Search for the same purpose.

Thank you :).
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GMAT Club test M25: # 31 10 Nov 2009, 05:10
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Thanks dzyubam! I will take care of it going further.

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