Compute $\lim_{n \to \infty}\prod_{k=1}^n (\frac{k}{n})^{1/n}$

Question

Compute $$\lim_{n \to \infty}\prod_{k=1}^n (\frac{k}{n})^{1/n}$$
I tried to compute term by term, and the limit of each term for $k$ gives me 1. Thus, I assume the product of 1 is 1. However, Wolfram Alpha gives an answer of $1/e$. How do I compute this limit?

PS: I tried to make use of the Stirling's formula for $n!$, but I can't make it work.

Answer 1

$$\ln(L)=\lim_{n\to\infty}\sum_{k=1}^n \frac{1}{n}\ln(\frac{k}{n})=\int^1_0\ln(x) dx =-1$$

$$\implies L=e^{-1}$$