GMAT Exponents

[Priester]

Hi Guys,

I received the following question during one of the GMAT practice tests:

[2^(4-1)^2]
---------------
[2^(3-2)]

I thought this would be fairly straightforward, but I got it wrong!!! I did 4-1 equals 3 therefore, on the top of the equation you get (2^3)^2 which will equal 2^6. And then on the bottom: 2^1. Therfore, subtracting the top from the bottom, you get 2^5. This is wrong. The official answer is 2^8. I tried getting their answer, but the only way I could would be to square 3, when its 2^3^2. However, I thought when you have an exponent raised to another exponent, it is simply multiplication.

Please help!!!
Thx.

[sankruth]

2^(3^2) is not the same as (2^3)^2.

2^(3^2) = 2^9

(2^3)^2 = 2^6

Hope this helps!

[sibbineni]

[2^(4-1)^2]
---------------
[2^(3-2)]


The official answer is 2 ^8

let take the numerator [2^(4-1)^2]
[2^3^2]
let us consider x=3^2
2^x

evaluate for x if 3^2=3*3=9

so x=9 then
2^x=2^9
but not [2^3^2]!=[2^6] because it determines that 3 to the power of 2 not the base term

The denominator is 2^1


2^8/2^1
a^x/a^y = a^(x-y)
the answer is
2^7