exponent problem in gmat prep--- image attached..confused...

[tigerwoods]

http://www.postimage.org/image.php?v=PqHq8Ii

i had to post the image cause I didnt know how gmat got 2^8 as the answer... and the terms in this problems make searching the forums difficult.

the problem is better seen in the image

the answer choices are

2^8
2^7
2^6
2^5
2^4

It should be 2^5.... according to me....

[twothousandeight]

numerator : 2 raise to power (4-1)sq is equal to 2 raise to power 9
denominator: 2 raise to power ( 3-2) is equal to 2 raise to power 1

since bases are same u can subtract and result would be 2 raise to power 8, simple, was not it

[tigerwoods]

thank you 2008.......

well I get it you can square it , but I got confused with the exponent rule (2^3)2= 2^6........

in exponents when you are raising the power I thought you had to multiply and not square it........

for ex

(x^2)^4 = (x^2)(x^2)(x^2)(x^2)
= (xx)(xx)(xx)(xx)
= xxxxxxxx
= x8

by using the power rule we would have (x)2^4= x ^ 2^4= x^16

so when we raising exponents to the power do we multiply or raise the power to the power.....

[RonPurewal]

thank you 2008.......

well I get it you can square it , but I got confused with the exponent rule (2^3)2= 2^6........

in exponents when you are raising the power I thought you had to multiply and not square it........

for ex

(x^2)^4 = (x^2)(x^2)(x^2)(x^2)
= (xx)(xx)(xx)(xx)
= xxxxxxxx
= x8

by using the power rule we would have (x)2^4= x ^ 2^4= x^16

so when we raising exponents to the power do we multiply or raise the power to the power.....

ahhhhhh ok, i see what you're doing here. you thought that you were supposed to take 2^(4-1) and square THE WHOLE THING.
that's not what you're supposed to do.

the giveaway is the parentheses just around (4-1). that means that (4-1) is being squared, and then you raise 2 to that whole power. (if 2^(4-1) were being squared, then you would see larger parentheses around the entirety of 2^(4-1).)

but yeah, i feel your pain on this one. ugly ugly ugly.