Answer
$y=(x-1)^{\frac{2}{3}}-1$
$\:$
$ $
Work Step by Step
Moving the graph down by $\ 1\ $ units will change the $\ y\ \rightarrow\ y+1$. And moving it to the right by $\ 1 \ $ units will change the $\ x\ \rightarrow\ x-1.$
So the equation of the shifted graph would be:
$y+1=(x-1)^{\frac{2}{3}}$
$y=(x-1)^{\frac{2}{3}}-1$
