Regular expression $(a^{*}b^{*})^{*} = \left( a+b \right)^{*}$ proof Im having a lot of trouble proving that for the Regular expression $R_{1} = \left( a^{*} b^{*} \right)^{*}$ and $R_{2} = \left( a+b \right)^{*}$ that $L \left( R_{1} \right) = L \left( R_{2} \right)$. I was wondering if anyone could help me with this? thanks
First prove that every word in R1 is also in R2; then prove that every word in R2 is also in R1.  Spend some time on each and see what progress you can make.