Derive the $n^{th}$ raw moment of the Beta Distribution from $n^{th}$ raw moment of the Gamma Distribution

Derive the $n^{th}$ raw moment of the Beta Distribution from $n^{th}$ raw
moment of the Gamma Distribution

Exploiting the independence of $U=\frac{X}{X+Y}$ and $V=X+Y$ , the fact
that $X$ and $Y$ are both Gamma, $X\sim \Gamma(\alpha,0,1)$ and $Y\sim
\Gamma(\beta,0,1)$, and the $n^{th}$ raw moment of the Gamma Distribution
, derive the $n^{th}$ raw moment of the Beta Distribution .
I know the $n^{th}$ raw moment of $X\sim \Gamma(\alpha,0,1)$ is
$$\mu_n^{\prime}=\frac{\Gamma(\alpha+n)}{\Gamma(\alpha)};\quad,n=1,2,...$$
But what will be the $n^{th}$ raw moment of the Gamma Distribution of the
above problem to derive the $n^{th}$ raw moment of the Beta Distribution ?
Why do i need to assume the independence of $U=\frac{X}{X+Y}$ and $V=X+Y$
to derive the $n^{th}$ raw moment of the Beta Distribution ?
Or,i think i have not understood the question properly.