9. Given that $\left\{a_{n}\right\}$ is a geometric sequence with all terms being positive, and $a_{50}, a_{51}$ are the two distinct solutions of the equation $100 \lg ^{2} x=\lg (100 x)$. Find the value of $a_{1} a_{2} \cdots a_{100}$.
$$
\begin{array}{l}
100 \log ^{2} x=\log (100 x) \Rightarrow 100 \log ^{2} x-\log x-2=0 \Rightarrow \log a_{50}+\log a_{51}=\frac{1}{100} \\
\Rightarrow a_{50} a_{51}=10 \frac{1}{100} \text {. Let } M=a_{1} a_{2} \cdots a_{100} \Rightarrow M^{2}=\left(a_{1} a_{100}\right)^{100}=\left(a_{50} a_{51}\right)^{100}=10 \\
\Rightarrow M=\sqrt{10}, \text { so } a_{1} a_{2} \cdots a_{100} \text { is } \sqrt{10} .
\end{array}
$$