For regular expressions $r$ and $s$ prove: $$(r^*s^*)^*=(r+s)^*$$
I guess I have to prove the equality of sets $(R^*S^*)^* = \left\{ x_1^{n_1}y_1^{m_1}x_2^{n_2}y_2^{m_2}... \mid n_i,m_j \in \mathbb{N_0},x_i \in R, y_j \in S \right\}$ and $(R \cup S)^* = \left\{ x_1^{n_1}x_2^{n_2}x_3^{n_3}... \mid n_i \in \mathbb{N_0},x_i \in R \cup S \right\}$ This seems simple enough.