If a and b are algebraic over a field F with degrees m and n, respectively, and m and n are relatively prime, then the extension degree [F(a,b):F] equals mn. Clarification is sought regarding whether a and b are indeed algebraic over F and if the notation F(a,b)=mn is intended to express [F(a,b):F]=mn. The relationship between the degrees of the extensions is questioned, particularly whether [F(a,b):F] equals the product of the individual degrees [F(a):F] and [F(b):F], which is generally false. Understanding the implications of the degrees being relatively prime is crucial in this context. The discussion emphasizes the need for precise definitions and conditions in algebraic field extensions.