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)