Determine $p,q$ and $r$ so that the order of the iterative method

$x_{n+1}=p{x}_n+\frac{aq}{x_n^3}+\frac{r{a}^2}{x_n^7}$

for $\sqrt[4]{a}$ becomes as high as possible. Also, determine the order of the iterative scheme for this choice of $p,q$ and $r.$