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

[abehrman]

The answers are:
a) 2^8
b)2^7
c)2^6
d)2^5
2)2^4


The correct answer is A, but I am confused because powers of powers require you to multiply the exponents. So 2^3^2 would be 2^6 / 2^1, shouldnt that be 2^5 not 2^8? In order to get 2^8 you must square the exponent 3, is this right?

Thank you very much.

[agha79]

My understanding was same as abehrman's understanding. Can someone please help?

[ryan.m.doyle]

This is can be confusing...
The first thing to look for is Parenthesis (think PEMDAS). Then look for exponents and work from the highest and work down...
(3^3)^3 = 3^(3^3) ? NO
(3^3)^3 = 27^3 = 19,683 or 3^(3*3) = 3^9 = 19,683
but it does not = 3^(3^3) = 3^27 = a big number

So (2^(4-1)^2) = 2^(3)^2 = 2^9
Not (2^(4-1)^2) = (2^3)^2 = 8^2

If the parenthesis were around (2^3) it would be (2^3)^2 = 8^2 = 64 or 2^(3*2) = 2^6 =64

Its hard to see without superscript but 2^2 is (2)^2 and 2^2^2 is (2)^(2)^(2)

Multiplying the exponents only works if it is in parenthesis:
(2^2)^2 = 2^(2*2) = 2^4 = 16
or (2^2)^2 = 4^2 = 16

Hope that helps.

[mschwrtz]

Ryan is perfectly correct. First, you should read x^a^b as x^(a^b), because of PEMDAS. Second, (x^a)^b does not equal x^(a^b), except when ab = a^b.

Offhand, I can't recall any actual GMAT questions involving expressions of the form x^a^b. I would speculate that such questions would distinguish very badly between good test-takers and poor test-takers. Notice the word 'speculate' though.