SOLUTION: 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? thanks,

Algebra ->  Exponents -> SOLUTION: 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? thanks,      Log On


   

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?

thanks,
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
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?
%28q%5E3p%5E2%29%2Fr%5E2+=+s%5En

is true if and only if

q%5E3p%5E2+=+r%5E2s%5En

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 

n can only be 3.

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

Edwin