2. Given that $P(x, y)$ is a point on the ellipse $\frac{x^{2}}{8}+\frac{y^{2}}{2}=1$. Then the minimum value of $3^{-x}+9^{y}$ is $\qquad$ .
2. $\frac{2}{9}$.

According to the mean inequality, we have
$$
\begin{array}{l}
x-2 y \leqslant\left(\frac{x^{2}}{4}+1\right)+\left(y^{2}+1\right) \\
=2\left(\frac{x^{2}}{8}+\frac{y^{2}}{2}\right)+2=4 .
\end{array}
$$

On the other hand,
$$
\begin{array}{l}
3^{-x}+9^{y}=3^{-x}+3^{2 y} \\
\geqslant 2 \sqrt{3^{-(x-2 y)}} \geqslant 2 \sqrt{3^{-4}}=\frac{2}{9},
\end{array}
$$

where the equality holds if and only if $x=2, y=-1$.
Therefore, the minimum value of $3^{-x}+9^{y}$ is $\frac{2}{9}$.