Commutator in hyperalgebras....

If I need to calculate some bracket like [x_\beta^{(n)}, x_\alpha^{(m)}], how should I proceed? Can I proceed doing the calculation to [x_\beta^{n}, x_\alpha^{m}] , then I multiply by \frac{1}{n!m!} and try to write the result in a divided power notation???

Thanks.

I meant: Let g a finite-dimensional simple Lie algebra, {\alpha_i,...,\alpha_n} the set of positive roots. Take U_Z(g\otimes C[t,t^{-1}]) the hypearlgebra associated to g\otimes C[t,t^{-1}] over some field of positive characteristic. It is well-known that there exist an integral form for U_Z(g) and it is generated by (x_{\alpha,r}^-)^{(k)} where k>0, r\in Z and \alpha is a positive root. So, how to calculate [ (x_{\alpha,r}^-)^{(k)}, (x_{\beta,s}^-)^{(m)}] ???? Is it clear now?