The given algebraic expression is, \(\frac{8r^{1/2}s^-3}{2r^-2 x^4}\)
Calculation:
Simplify the given algebraic expression.
\(\frac{8r^{1//2}s^-3}{2r^-2 x^4} = 4r^{\frac{1}{2}-(-2)}s^{-3-4}\)

\([\therefore] \frac{a^m}{a^n} = a^{m-n}\)

\(= 4r^{\frac{1}{2} +2} s^{-7}\)

\(= 4r^{\frac{5}{2}} s^-7\) Therefore, the simplification of the given algebraic expression is \(4r^{\frac{5}{2}}s^{-7}\).

\([\therefore] \frac{a^m}{a^n} = a^{m-n}\)

\(= 4r^{\frac{1}{2} +2} s^{-7}\)

\(= 4r^{\frac{5}{2}} s^-7\) Therefore, the simplification of the given algebraic expression is \(4r^{\frac{5}{2}}s^{-7}\).