prove that if $a_1 a_2\cdots a_n=1$ implies $a_1^{n-1}+a_2^{n-1}+\cdots a_n^{n-1}\geq \frac{1}{a_1}+\frac{1}{a_2}+\cdots+ \frac{1}{a_n}$
How to prove $a_1^m + a_2^m + \cdots + a_n^m \geq \frac{1}{a_1} + \frac{1}{a_2} + \cdots + \frac{1}{a_n}$