Let a be a non zero number and m and n be integers. Prove by induction that:

(1) $\displaystyle a^{m+n} = a^{m} a^{n}$

(2). $\displaystyle {(ab)}^{n} = {a^n}{b^n}$

can anyone explain me the basis and inductive steps here?

Do I have to start by supposing $\displaystyle n=0$ in (1) and

$\displaystyle n=1$ in (2)?

what about the inductive step?