SOLUTION: if p, q, r, and s are prime numbers and (q^3.p^2)/r^2 = s^n, what is the value of n?

Algebra ->  Divisibility and Prime Numbers -> SOLUTION: if p, q, r, and s are prime numbers and (q^3.p^2)/r^2 = s^n, what is the value of n?      Log On


   

Question 978273: if p, q, r, and s are prime numbers and (q^3.p^2)/r^2 = s^n, what is the value of n?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Prime factorization is unique except for the order of factors.

n could only be 3 because

(q^3*p^2)/r^2 = s^n

then
q^3*p^2= r^2*s^n

There are 5 primes multiplied together on the left, so
there must the same 5 primes multiplied together on the right.

In fact p=r and q=s, and of course n=3.

Edwin