Rewrite in simplest radical form:

First one.....convert to exponential form....

(50r^2s^4)^(1/2)  =   ( 25 * 2 * r^2 * s^4)  =  (25)^(1/2) * (2)^(1/2) * (r^2)^(1/2) * (s^4)^(1/2) =

5 * (2)^(1/2) * r * s^2  =

5 r s^2 √2

Second one      3 √[18x^3]  =  3  √ [ 9 * 2 * x^3 ]  =   3 *(9)^(1/2) * (2)^(1/2) * (x^2)^(1/2) * (x)^(1/2)  =

3 * 3 * 2^(1/2) * x * (x)^(1/2)  =

9 * x * 2^(1/2) * (x)^(1/2)  =

9x  √ [ 2x ]