DIFFICULT GMAT MATH - URGENT HELP

[kuemura]

PowerPrep Math PS - Pls help!
Hi, Please help the below:

(1/5)^m x (1/4)^18 = 2(10)^-35

answer: m = 35

Can you explain why you get this for the answer?

[clock60]

(1/5)^m=(5^-1)^m=5^-m
(1/4)^18=(4^-1)^18=(2^-2)^18=2^-36
(10)^-35=(2*5)^-35=(2^-35)*(5^-35)
(2^-36)/2^1=2^(-36-1)=2^-37 (i try to get rid off 2 from right part)
(5^-m)*(2^-37)=(2^-35)*(5^-35)
it is very stange but i can`t cancel exponent 2 totaly and i can`t find my mistake
(5^-m)*(2^-2)=(5^-35)
kuemura are you sure that you write all numbers correctly????

[kuemura]

Hi there, apologies there was a mistake.

(1/5)^m x (1/4)^18 = 1/2(10)^35

Would appreciate any explanation on the corrected one above.

[kuemura]

(1/5)^m x (1/4)^18 = 1/2(10)^-35

This one is the correct question.

[Chandru42]

there is a small error in the Q

[muralik]

Originally Posted by kuemura

Hi there, apologies there was a mistake.

(1/5)^m x (1/4)^18 = 1/2(10)^35

Would appreciate any explanation on the corrected one above.

5^ -m x 4^-18 = 2^-1 x 10^-35

5^-m x (2^2)^-18 = 2^-1 x(2 x5)^-35

5^-m x 2^(2x-18) = 2^-1 x 2^-35 x 5^-35


5^-m x2^-36 = 2^(-1 -35) x 5^-35



5^-m = 5^-35

-m = -35
m =35

hope this helps

[kuemura]

muralik,

you are a genius (or am i too dumb?!) either way crystal clear. many thanks.
i see the importance of factoring out to cancel as much as possible.

[Mahendra700]

yes i too got m = 35..good question