Prove the following language is regular using closures How can I prove this language is regular using just closures and homomorphism?
$$
L = \{a_1b_1a_2b_2\dotsm a_nb_n \mid a_i \in L_1 , b_i \in L_2\}
$$
and we know $L_1$ and $L_2$ are regular.
To get you started, consider a restricted version of your languge: 
$$
L'=\{ab\mid a\in L_1, b\in L_2\}
$$
Notice that $L$ is the concatenation $L'=L_1\circ L_2$. Can you carry on from there?