Show that NP is closed under concatenation.
This is a homework problem and I would appreciate some guidance. I began by saying the following:
Let $A$ and $B$ exist in NP. Let $V_1$ and $V_2$ be verifiers for $A$ and $B$, respectively.
Is it as simple as saying build two NTMs $M_1$ and $M_2$ that decide $A$ and $B$ and then concatenate them and build a new machine to decide?