This infinite sum raised to a power can be expanded by distributing terms in the standard way. In doing so, the various powers of x multiplied together will create a series in powers of x involving \(x^0, x^1, x^2, ...\text{.}\) To detemine the final coefficients notice that the number of time \(m^k\) will appear in this product depends upon the number of ways one can write k as a sum of nonnegative integers.