How to show that $\prod_{n=0}^{\infty}\Gamma^{{k-1\over n+1}}(n+x)=\Gamma(x)\prod_{n=1}^{\infty}(n+x)^{{1\over k^n}}?$

Question

Let

$$P=\prod_{n=0}^{\infty}\Gamma^{{k-1\over n+1}}(n+x)$$

$$Q=\Gamma(x)\prod_{n=1}^{\infty}(n+x)^{{1\over k^n}}$$

$x\ge1$ and $k>1$

Where $\Gamma(n)$ is the Gamma function

How do we show that $P=Q?$

I haven't even got a clue where to begin.

I believe I got the idea of the products $P$ and $Q$ from observing Knar's formula.

It is quite long ago, so there is no other hints I could added to help.