Solve the following system of equations:

$$
\sqrt[3]{a^{y}}=\sqrt{\frac{a^{13}}{a^{x}}}
$$

$$
\sqrt[7]{a^{3 x}} \cdot \sqrt[9]{a^{4 y}}=a^{7}
$$
From (1):

$$
\frac{y}{3}=\frac{13-x}{2}
$$

From (2):

$$
\frac{3 x}{7}+\frac{4 y}{9}=7
$$

Solving this system of equations: $x=7, y=9$.

(Alfréd Haar, VII.o. t., Budapest.)

Number of solutions: 25.