I am studying the free notes/practice tests at a site associated with/hosted [and run] by lamar university: the link is as follows

http://tutorial.math.lamar.edu/

Now, there is a problem (number seven, integer/exponents section) whose answer is unclear to me: here is the link to the solution's page:

http://tutorial.math.lamar.edu/Solutions/Alg/IntegerExponents/Prob7.aspx

Can someone explain to me how variable "n" is chosen to be the denominator, and "m" the numerator?"

It is not immediately obvious to me, and the explanation would be greatly appreciated.

Also, if the decision is "up in the air", and either variable would suffice (as seems to be the case: at least, in my opinion), how likely is such a problem to be on standardized tests (for example, the "clep" and other "credit by examination" tests), and, furthermore, how is there any way to know you are getting the answer right if two answers are, technically, viable and correct?

Again, any and all help and suggestion is greatly appreciated.

Thank You

Sincerely,

rjs