Choice A is the correct answer. Calculate both values.

1. Calculate $e^\pi$: $e^{3.14159} \approx 23.14$.
2. Calculate $\pi^e$: $3.14159^{2.718} \approx 22.46$.
3. Comparison: $23.14 > 22.46$, so $e^\pi > \pi^e$.

💡 Strategic Tip: This is a famous inequality: $e^\pi > \pi^e$.

Choice B is incorrect because$\pi^e$ is slightly smaller. Choice C is incorrect because they are close but not equal. Choice D is incorrect because we can calculate both.