Stuck on mba.com exponent problem

[suzeemunkee]

I really wish mba.com provided answer explanations to their practice tests! Here's one I'm stuck on:

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

I get 2^5. . . but the answer is 2^8. Why??

Thanks for your help! [/list]

[Gmat_War]

(4-1)^2= 3^2=9
Therefore 2^9/2^(1)
=>2^(9-1)=2^8

[suzeemunkee]

(4-1)^2= 3^2=9
Therefore 2^9/2^(1)
=>2^(9-1)=2^8

Thanks for the quick reply! I'm still a bit confused because I thought to calculate an exponent of an exponent, you multiply the exponents? For example, (2^3)^2 = (2*2*2)(2*2*2) = 2^6

[indiantiger]

Original statement = 2^(4-1)^2 / 2^(3-2) , we need to simplify this

Lets take denominator first, its more simple
=> 2^(3-2) = 2^1------(D)

Lets take numerator now

=>2^(4-1)^2
=>2^3^2
now here the exponent ^2 has base 3 not 2^3, so this becomes:
=>2^9 ( as 3^2 = 9)------(N)

From (N) and (D)
(2^9) /(2^1)
= 2^8

I hope this helps.

[suzeemunkee]

Ah, OK. That makes sense. Thank you both for your help!

[iastah]

I think you're main confusion is on order of operations

if it was (2^3)^2, then, yes, your answer would be right

but in this case it's not that way. it's 2^3^2

which by order of operation you square the 3 first making the equation simplify to 2^9

[suzeemunkee]

I think you're main confusion is on order of operations

if it was (2^3)^2, then, yes, your answer would be right

but in this case it's not that way. it's 2^3^2

which by order of operation you square the 3 first making the equation simplify to 2^9

Ohh, OK. That makes sense why I kept getting the wrong answer. I appreciate your help!!

[Patrick_GMATFix]

I really wish mba.com provided answer explanations to their practice tests! Here's one I'm stuck on:

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

I get 2^5. . . but the answer is 2^8. Why??

Thanks for your help! [/list]

hey Suzee. I hope the explanations provided made sense to you. I've fallen for this very question myself. Unless parentheses are used to suggest a different order, this is handled as you would with complex fractions; you start farthest away from the main line and work your way back. This is GMATPrep question 1075. If you have trouble with complex exponents, you could use the Drill Engine to run timed drills with settings: topics='exponents & roots' and difficulty='600-700 AND 700+'

Good luck,
-Patrick

[suzeemunkee]

Thanks, Patrick. I'm definitely going to work on those exponent problems.

Really appreciate all your guys' quick responses! You guys are really great.