Itô's lemma in use

Let $W$ be a standard Brownian motion and $S$ follow (8.15). (a) Compute $d(W_t^2)$ and deduce $\mathbb E[W_t^2]=t$ using the martingale property of the Itô integral. (b) Compute $d(S_t^n)$ for an integer $n\ge1$ and deduce $\mathbb E[S_T^n]=S_0^n\exp\{(n\mu+\tfrac12n(n-1)\sigma^2)T\}$. Check against the lognormal moment formula. (c) Show that under (8.20) the process $e^{-(r-q)t}S_t$ is a martingale, and that under (8.15) it is a martingale only if $\mu=r-q$.