On a radical extension of the field of rational functions in several variables

Let F be a field and let F(X1,…,Xn) the of rational functions in n variables X1,…,Xn over F. T=X1+⋯+Xn∈F(X1,…,Xn) m positive integer such that charF∤m. Is it possible to express each Xi as function X1m…,Xnm T F? It is not difficult prove this can done but another matter show how done. We answer above question affirmatively with nonconstructive proof constructive proof.