First of all, welcome to the GMATClub ! :D

Following your posts focussed on this sort of question, I would like to detail u the whole process

This question is a classical one of the GMAT

... The hidden structure behind some flips or simplications is like this:

x^a * y^b = x^d * y^e with x != y

As in an equation, the right side is always equal to the left side, we can indenty and then equalize expression in x and in y

So,

o x^a must be equal to x^d

o y^b must be equal to y^e

Then,

o a=d

o b=e

That said, let us try to rewrite your problem in an equation to identify expressions from the left side to the ones from the right.

To continue the image, set x=1/4 and y=1/5 in your mind

... We have to recreate x and y in the right side of the equation.

(1/4)^n * (1/5)^18 = (1/20)^35

= (1/4 * 1/5)^35

= (1/4)^35 * (1/5)^35

Thus, n=35.

But, u could see that (1/5)^18 cannot be equal to (1/5)^35

... That's where I think we have a typo in this question

... Because the GMAT would never ask u to solve it like this:

(1/4)^n * (1/5)^18 = (1/20)^35

<=> (1/4)^n = (1/4)^35 * (1/5)^17

<=> n * ln(1/4) = 35*ln(1/4) + 17*ln(1/5)

<=> n = 35 + 17*ln(5)/ln(4)