Recursive and regular languages
Tips.


Any (infinite) unary language has regular prefix language.
$L_1 = a \cdot K$ and similary 
$L_2 = b \cdot K$  where $K$ is a well-chosen horrible language.  


Question.

What is unary($L$)? If it is what I think, there is an easy example. Powers of two are not context-free: $\{ a^{2^n} \mid n\ge 1\}$.