GMAT TIGER wrote:

Bluepic wrote:

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

a) 2^8

b) 2^7

c) 2^6

d) 2^5

e) 2^4

Please show work as I got this answer wrong.

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

= 2^(3)^2 / 2

= 2^6 / 2

= 2^5

I thought that way (2^8) too but ended with 2^5 because I remember a question: If X=10^100 , X^X = 10^K. What is K= ?

The following notes are by walker:

**Quote:**

(x^y)^z=x^(y*z) - is a key point. There are no any other additional formula.

more examples:

(2^3)^5=8^5=32768 or

(2^3)^5=2^(3*5)=2^15=2*2^14=2*4^7=2*4*4^6=8*16^3=32768 or

(2^3)^5=2^(3*5)=(2^5)^3=32^3=32768

√x=4. What is x^3?

x^3=x^(3*2*1/2)=x^(6*1/2)=(x^1/2)^6=(√x)^6=4^6

in the case of (10^100)^(10^100):

(10^100)^(10^100)=10^(100*(10^100)) = 10^(10^2*(10^100)) = 10^(10^(2+100))) = 10^(10^102)=10^k ==> k=10^102

How one should relate this problem with the above notes:

when is 2^(4-1)^2 = 2^6 and when is 2^(4-1)^2 = 2^9?

any clear rule?

thanks

_________________

Verbal: http://gmatclub.com/forum/new-to-the-verbal-forum-please-read-this-first-77546.html

Math: http://gmatclub.com/forum/new-to-the-math-forum-please-read-this-first-77764.html

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT