Prove that L $\in$ NP implies L* $\in$ NP
Lets hop back to the definition of a NP language, there exists a non-deterministic Turing machine NTM that halts when given $x$. 

It's not that much work to create a non-deterministic Turing machine that first splits the input string into parts non-deterministically and then simulates running NTM on each of the parts and only halts when all parts make the NTM halt.