Given the equation \(p = \sqrt{\frac{rs^3}{t}}\), we want to express \(r\) in terms of \(p\), \(s\), and \(t\).

Let's solve for \(r\):

Start with the given equation:

\(p = \sqrt{\frac{rs^3}{t}}\)

Square both sides to eliminate the square root:

\(p^2 = \frac{rs^3}{t}\)

Now, solve for \(r\):

\(r = \frac{p^2 t}{s^3}\)

So, the expression for \(r\) in terms of \(p\), \(s\), and \(t\) is:

\(r = \frac{p^2 t}{s^3}\)

The correct answer is \(\frac{p^2 t}{s^3}\).