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.