GMAT Prep exponents question

[amaanb]

Hey all,

Been a lurker here for a while..have the GMAT tomorrow so am in hardcore study mode!

Was doing GMATPrep and came across a simple question that threw me for a curve ball:

2^((4-1)^2) / 2^(3-2)

A) 2^8
B) 2^7
C) 2^6
D) 2^5
E) 2^4

Writing it out makes it a lot clearer to understand.

To tackle the numerator, I subtracted 1 from 4 and got:

2^((4-1)^2)
=2^((3)^2)

I then multiplied the exponents and got
2^((3)^2)
=2^6

The denominator is fairly easy - simly subtract:
2^(3-2)
=2^1
=2

This gave me:
2^6 / 2^1
=2^5


The OA is A) 2^8 however. I recognized where I made the mistake - in the numerator. It should be:

2^((4-1)^2)
=2^[(4-1)*(4-1)]
=2^(3*3)
=2^9

My question is, what exactly is the rule for nested exponents? I thought it was simple as multiplying the exponents. In this question, this doesn't seem to be the case. One exponent is fully distributed instead of being multiplied.

Thanks for any help!

[NikolayZ]

Hi Amaanb.
In this case you just mixed up nested exponent with a power of an exponent.

For example.

(a^2)^4=a^2*4 - nested; you raise to a power of 4 the expression (a^2).
(a^(2^4))=a^16, since 2^4=16. In this case, you raise to a power 2, which is the exponent of a.

Hope it helps.

[amaanb]

thanks!