$($a$)$ Give a regular expression for a language Lsube${}^{**}$ which satisfies the following conditions

$|L|>0$

$|L^{**}|$ is finite

$($b$)$ Consider a statement about arbitrary languages

$A{A}_{L,\text{M}\text{s}\text{u}\text{b}\text{e}{}^{**}}(LM{)}^{**}=L^{**}{M}^{**}$

Prove or disprove it $($when providing a counterexample, $L,M$ should be given as regular expressions$).$

$($c$)$ Provide a regular expression for the following language over $=\{0,1\}$

$L=\{xin|$ the number $1\text{'}sinxis$ a divisible $by4\}$

Prove that your expression captures precisely the language $L.$