1. The problem statement, all variables and given/known data If [itex]gcd(f(x),g(x)) = 1[/itex] and m,n ∈ ℕ, show that [itex]gcd(f(x)^m, g(x)^n) = 1[/itex]. 2. Relevant equations 3. The attempt at a solution So I had previously proved this for non-polynomials: gcd(a,b)=1 then gcd(a^n,b^n)=1 Proof: a = p1*p2*...*pn b = p1*p2*...*pm then a^n = p1^n*p2^n*...*pn^n b^n = p1^n*p2^n*...*pm^n Since a and a^n have the same prime factors and b and b^n have the same prime factors and a and b are relatively prime then a^n and b^n are relatively prime. I guess, I am looking at this question from the same point of view. Is there a difference here with polynomials? Why would there be?