2. A person writes the number $2^{x} 9^{y}$ as a four-digit number $2 x 9 y$, by substituting $x$ and $y$ with positive integers less than 10, and it turns out that $2 x 9 y=2^{x} 9^{y}$. What are the values of $x$ and $y$?
答: $\left\{\begin{array}{l}x=5, \\ y=2 .\end{array}\right.$

Answer: $\left\{\begin{array}{l}x=5, \\ y=2 .\end{array}\right.$