Example 2. The sequence $\left\{a_{n}\right\}$ satisfies $a_{n+1}=2^{n} a_{n}$, $a_{1}=1$, find the general term formula.
\begin{array}{l}\text { Sol } a_{n}=a_{1} \prod_{\mathrm{k}=1}^{\mathrm{n}-1} \frac{a_{k+1}}{a_{k}}=\prod_{\mathrm{k}=1}^{\mathrm{n}-1} 2^{k} \\ =2 \frac{n(n-1)}{2} .\end{array}