Prove or disprove $,$ pls be concise

$($b$)$ For every natural number $k,$ if Lsube$\{0,1{\}}^{**}$ is recognized by a DFA with $k$ states, then there

also exists a DFA with $k$ states recognizing $(\frac{?}{\text{b}\text{a}\text{r}}(L){)}^{**}.$