12. Find all values of integers $x$ and $y$ satisfying $2^{3 x}+5^{3 y}=189$.
Answer: $x=2$ and $y=1$.
Solution: We have
$$
\begin{aligned}
2^{3 x}+5^{3 y} & =\left(2^{x}+5^{y}\right)\left(2^{2 x}-2^{x} 5^{y}+5^{2 y}\right) \\
& =(9)(21) \\
& =189
\end{aligned}
$$

Clearly, $(x, y)=(2,1)$ is the only solution pair to the equation.