Why is [F(a,b):F]=mn when a and b are algebraic of coprime degrees?

[johnson123]

Homework Statement

If a and b are algebraic over F of degree m and n, both relatively prime, then

F(a,b)=mn, (i.e. [F(a,b):F]=mn)

any comments are helpfull.

 

[morphism]

Your post is very incomplete. Are a and b algebraic over a field F? And by "F(a,b)=mn" do you mean "[F(a,b):F]=mn"?

In which case, that m and n are relatively prime is important. Are you trying to say that [F(a,b):F]=[F(a):F][F(b):F]? This is false in general (why?).