GMATPrep Exponents

rvess wrote:
(1/5)^m x (1/4)^18 = 1/2(10)^35, then m= ?

Hi rvess,

I think there is a typo in the question.

The question would be

(1/5)^m (1/4)^18 = (1/2)(1/10)^35, then m= ?

Now convert the fractions in exponents.

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

Simplify 4 = 2 ^ 2 and 10 = 5* 2

or 5 ^ (-m) * (2)^ (-18*2) = 2 ^ (-1) * (5 * 2)^ -35
or 5 ^ (-m) * (2)^ (-36) = 2 ^ (-1 - 35) * (5 )^ -35
Since the powers of 2 on both sides are so divide it and you are left with only base 5 on both sides
or 5 ^ (-m) = (5 )^ -35
Since base are same so equate the exponent
-m = -35
or m =-35

Hope it helps.

Confirm the question please

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

(1/5)^m.(1/4)^18=5^35

5^-m.(1/4)^18=5^35

20^-m.(1)^18=20^35

20^-m=20^35
-m=35 or m=-35


Hope it helps.

Paresa

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

(1/5)^m.(1/4)^18=5^35

5^-m.(1/4)^18=5^35

20^-m.(1)^18=20^35

20^-m=20^35
-m=35 or m=-35


Hope it helps.

Paresa

its_me07 wrote:(1/5)^m.(1/4)^18=(1/2)(10)^35

(1/5)^m.(1/4)^18=5^35 Where did 2 and 10 go? (10 ^35)/2 = 2^34 * 5 ^ 35

5^-m.(1/4)^18=5^35

20^-m.(1)^18=20^35 I am not sure where did remaining powers 4 go ? if you have taken m powers from 18 then 4 will still have 18-m powers left....Correct me if I am wrong here but I guess the question itself is a typo

20^-m=20^35
-m=35 or m=-35


Hope it helps.

Paresa

I am a bit confused...either this calculation is done in haste or I am missing something please clarify ?

Thanks
Komal

Thank you Joshi and Paresa for breaking everything down, makes sense now!

To clarify, the question should have been as Joshi typed it;
(1/5)^m (1/4)^18 = (1/2)(1/10)^35, then m= ?

(1/5)^m*(1/4)^18=(1/2)(1/10)^35
(1/5)^m*(1/2)^36=(1/2)(1/10)^35

therefore comparing on both sides of the equation,
(1/5)^m*(1/2)^35 (1/2)=(1/2)(1/10)^35 mere observing
(1/5)^m*(1/2)^35 =(1/10)^35 since 5*2=10

Hence m shud be 35 .

Thanks
Senthil

m=35 or -35?

We are getting the answer as m = -35.

Maybe, a mistake while typing the problem.


AJ.

m = 35 as the exponent is in the denominator