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What is a ^b ^c ?

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Re: What is a ^b ^c ?

by Vemuri » Mon Mar 30, 2009 2:01 am
a^b^c can be interpreted as (a^b)^c ==> a^bc

So, a^b^c^d^e ==> a^bcde
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by sacx » Mon Mar 30, 2009 2:21 am
I think it woud be interpreted as a ^(b^c)

eg: 3^2^3 = 3^(2^3)
= 3^8
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Re: What is a ^b ^c ?

by Ian Stewart » Mon Mar 30, 2009 6:32 am
vittalgmat wrote:How is a ^b ^c interpreted?

(a^b)^c OR a ^(b^c) ?

More generally how can I solve something like a^b^c^d^e ?
You don't often see expressions written this way, but if there are no brackets, then a^b^c means a^(b^c), and not (a^b)^c. So, if you did see something like 3^2^5, that means 3^32, and not 3^10. Of course, far more often you will have brackets in expressions like this - you're much more likely to see, or to need to work with, (3^2)^5 on your test.

I'd wager a lot of money you will not see something like a^b^c^d^e on your test, but if you did, there's not much you could do with that, if you have letters in the expression. If you saw something with numbers like:

2^2^2^2^2

you could work out the value of that expression as follows (start from the top and work backwards) :

2^2^2^2^2 = 2^(2^(2^(2^2))) = 2^(2^(2^4)) = 2^(2^16) = 2^65536

which helps to illustrate why you're not going to see something quite this complicated on the test - the answer will be too awkward to work with.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by vittalgmat » Mon Mar 30, 2009 6:08 pm
Thanks a lot Ian

Greatly appreciate it.

rgds
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by gmat740 » Mon Mar 30, 2009 8:36 pm
a^b^c can be interpreted as (a^b)^c ==> a^bc

So, a^b^c^d^e ==> a^bcde


Please note this is a very very Wrong way of approach

See the bold face

You are making a exponential term a multiple!!
Is it justified??

Well I believe No matter How many exponents be there,

As a rule

We Must start solving from upwards to downwards reaching the base

Eg: 4^2^3^2 = 4^2^9 = 4^512

I hope this makes more sense now.

Karan
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by cramya » Mon Mar 30, 2009 9:24 pm
Hi Vittal,
Hope u r doing well!


(a^b) ^ c = a^ (b*c)

and in reverse

a^(b*c) can be transformed in to (a^b)^c or (a^c)^b depending on what manipulation is required in the problem.

As Ian said if there are no braces u start working from right to left.

I think there was a GMAT PREP problem something similar to

2^2^3 or something.( u will do 2^3 first and then raise 2 to that answer)

Nice question!


Ian, thanks again for a good explanation.



Regards,
CR
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by vittalgmat » Mon Mar 30, 2009 9:55 pm
Thanks Cramya,
I am doing well... slowly getting back to GMAT grind. Bad economy makes it harder to get free time to work on GMAT..
I am spending more time on V hence I am not very active in Math forum..

keep in touch
-V
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