P2860
By hypothesis, $a$ satisfies
\begin{equation}
a^N
= \prod_{n = 1}^N a
= \prod_{n = 1}^N x_n
\end{equation}
Raising both sides to power $1/N$, we obtain
\begin{equation}
a
= (a^N)^{1/N}
= \left( \prod_{n = 1}^N x_n \right)^{1/N}
\end{equation}
$\square$
