Constraints? Really?

Let $a$ , $b$ , $c$ , and $d$ be reals such that $1\le a \le b \le c \le d \le 9$ . Find the sum of the minimum and the maximum value of

$\large (a-1)^4+\left(\frac ba -1\right)^4+\left(\frac cb -1\right)^4+\left(\frac dc -1\right)^4+\left(\frac {32}d -1\right)^4$

If the answer equals to ${ m }^{ n }+p{ (\sqrt { q } -r) }^{ n }+\dfrac { { s }^{ n } }{ { q }^{ 2n } }$ , where $(s,q)=1,(q,r^2)=1,\sqrt{m}\notin { Z }^{ + }$ and that $m,n,p,q,r,s$ are positive integers, find the product $mnpqrs$ .