Is there any language for which $\overline{L^*}=\big(\overline L\big)^*$? This question was asked in peter linz exercise. I have tried languages such as $\phi,\epsilon,\Sigma^*$.
No, thanks for Ariel's correction, since for every $L$ it holds that $\epsilon \not\in \overline{(L^*)}$  and $\epsilon \in (\overline{L})^*$ and therefore $ \overline{(L^*)}\neq (\overline{L})^*$