Question 33613
When you rationalize the denominator, you are basically manipulating the expression so there is no square root in the denominator.  Lets rewrite the problem to the following:
{{{(sqrt (25p^7))/(sqrt(r))}}}
We simplify the top first
{{{sqrt (25p^7)}}} = {{{5p^3(sqrt(p))}}}
So {{{5p^3(sqrt(p))/sqrt(r)}}}
Next, multiply numerator and denominator by {{{sqrt(r)}}}

{{{(5p^3*sqrt(p)*sqrt(r))/(sqrt(r)*sqrt(r))}}} 
{{{(5p^3*sqrt(pr))/sqrt(r^2)}}} 
{{{(5p^3*sqrt(pr))/r}}}