show that $\lim_{t\rightarrow0^{+}}[\frac{1}{n}\sum_{i=1}a_{i}^{t}]^{1/t}$ is the geometric mean of $a_{1},a_{2},...,a_{n}$

Question

Let $a_{1},a_{2},...,a_{n}$ be any n positive real numbers. show that $\lim_{t\rightarrow0^{+}}[\frac{1}{n}\sum_{i=1}^{n}a_{i}^{t}]^{1/t}$ is the geometric mean of $a_{1},a_{2},...,a_{n}$