7. Given the sequence $\left\{a_{n}\right\}$ where all terms are positive, if for any positive integers $p, q$, there is always $a_{p+q}=a_{p} \cdot a_{q}$, and $a_{8}=16$, then $a_{10}=$
$a_{p+q}=a_{p} \cdot a_{q} \Rightarrow a_{n}=a_{1}^{n}$, thus $a_{8}=16 \Rightarrow a_{2}=2, a_{10}=32$.