Problem Solving

I am taking the GMAT in a couple of weeks. I am doing fine so far, but there are these two annoying questions, that, no matter how hard I try - I do not know how to solve! There are apparently some rules concerning exponents I have missed...


1. 5^21 x 4^11 = 2x 10^n.

The answer is n = 21, but have no idea how to get there.


2. 2^x - 2^(x-2) = 3(2^13)

The answer is x= 15, but again....????

I guess it is uneccessary to say that exponents is not my strongest side :=)

Thanks you for all your help!

Please use the search option before posting a new question . and make sure u post one question per thread...

1 st question

5^21 * 4^11 = 2*10^n

we can write 4^21 as (2^2)^11 which is 2^22

hence its 5^21* 2^22

we can write 2^22 as 2* 2^21 ( a^m+n = a^m* a^n)

hence its

5^21*2*2^21 which can be written as

2* ( 5*2) 21 ...( a^m * b*m = ab^m)


thus its

2* (10)^21 = 2*10^n

hence n = 21

Hope its clear...

2. 2^x -2^(x-2) = 3(2^13)

u shud know that a^m/a^n = a^m-n...

we have to use the above rule in this question

2^x - 2^x/2^2 = 3( 2^13)........... ( 2^(x-2) can be written as 2^x/2^2 using the rule i mentioned

take 2^x common

2^x ( 1-1/4) = 3 (2^13)

2^x(3/4 ) = 3 (2^13)

cancel off 3 on both the sides..

2^x= 4*2^13

4 can be written as 2^2

hence its
2^x = 2^15 ( a^m* a^n = a^m+n )

hence x = 15...