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,

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(20056) (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?



is true if and only if



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

RELATED QUESTIONS
if p, q, r, and s are prime numbers and (q^3.p^2)/r^2 = s^n, what is the value of... (answered by Edwin McCravy)

Yann writes down the first n consecutive positive integers, 1, 2, 3, 4, . . . , n − 1,... (answered by greenestamps)

If p - q = 5 and pq = 3, find the value of p² + q². ----- I've... (answered by noname9900)

If p, r, and s are three different prime numbers greater than 2, and n = p X r X s, how... (answered by edjones)

If p, r, and s are 3 different prime numbers greater than 2, and n= p x r x s then how (answered by vleith)

if p,r,and s are three different prime numbers greater than 2, and n= p x r x s, how many (answered by robertb)

If p, r and s are three different prime numbers greater than 2, and n= p*r*s, how many... (answered by solver91311)

`Line line 1, passes through points P(n, 4) and Q(1 2), Line 2, passes through points... (answered by josgarithmetic)

Let p, q, r and s represent the following: Determine the truth value of each statement.... (answered by ikleyn)