2. Let $p$ be a prime, $(a, b)=p$. Find $\left(a^{2}, b\right),\left(a^{3}, b\right),\left(a^{2}, b^{3}\right)$ and the possible values they can take.
2. $\begin{array}{l}a=p a_{1}, b=p b_{1},\left(a_{1}, b_{1}\right)=1 .\left(a^{2}, b\right)=p\left(p a_{1}^{2}, b_{1}\right)=p\left(p, b_{1}\right)=p, p^{2} . \\ \left(a^{3}, b\right)=p\left(a_{1}^{3} p^{2}, b_{1}\right)=p\left(p^{2}, b_{1}\right)=p, p^{2}, p^{3} . \\ \left(a^{2}, b^{3}\right)=p^{2}\left(a_{1}^{2}, p b_{1}^{3}\right)=p^{2}\left(a_{1}, p\right)=p^{2}, p^{3} .\end{array}$