$$ \sqrt[w]{x_{1}^{w_{1}} x_{2}^{w_{2}} \cdots x_{n}^{w_{n}}} $$
I am new in convex optimization, so I am confused to prove the equation. Given nonnegative parameters $w_i > 0$, $i=1, \ldots, n$ and $w = w_1 + \ldots + w_n$. Prove that the following function is concave in nonnegative $x_1, \ldots, x_n$. Thank you for your answer and help!