Determine which is bigger,`(1)/(pi)^(1/e) or (1)/(e )^((1)/(pi))`?

Explanation

To determine which of the two expressions \(\frac{1}{\pi^{1/e}}\) or \(\frac{1}{e^{1/\pi}}\) is larger, we can follow these steps:

### Step 1: Compare the bases
We know that \(\pi\) is greater than \(e\) (i.e., \(\pi > e\)). This is an important observation that will help us compare the two expressions.

**Hint:** Remember that if \(a > b\), then \(a^x > b^x\) for any positive \(x\).

### Step 2: Raise both sides to the power of \(e\) and \(\pi\)
...