Question 1038200
if p, q, r, and s are positive prime numbers, 
and (q^3p^2)/r^2 = s^n, what is the value of of n?
<pre>
{{{(q^3p^2)/r^2 = s^n}}}

is true if and only if

{{{q^3p^2 = r^2s^n}}}

is true.

The Fundamental Theorem of Arithmetic states
that every natural number greater than 1 can 
be written as a product of prime numbers, and 
this product is unique, except for the order of
the factors. 

There are 5 factors of primes on the left,
so there must be the same 5 factors of 
primes on the right, so 

<b>n can only be 3</b>.

In fact, though it wasn't asked for, 
p must equal r and q must equal s. 

Edwin</pre>