What does m= ? HOW TO DO IT QUICKLY

[gmatpup]

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

A. 17

B. 18

C. 34

D. 35

E. 36

Answer is D

[rijul007]

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

(1/5)^m * = (1/5)^35
m = 35

Option D

[gmatpup]

I am not seeing how you are getting from step 1 to 2 to 3...

could you explain further?

Thanks so much for the help!

[neelgandham]

Hi gmatpup,

Here is a step by step solution for your benefit.

Assuming 1/2(10)^35 is same as 1/(2*(10^35))

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

After cancelling the term (1/2)^(36) from both sides(i.e. Multiplying both sides with 2^36), we get
(1/5)^m = (1/5)^35

As bases are equal, powers should also be equal. So, m = 35. Answer is D

[ArunangsuSahu]

Clue: Take all fractions to their base Denominator and then equate both sides.

Answer is D