How can an expression written in either radical form or rational exponent form be rewritten into equivalent forms?

You can convert between radical and rational by remembering a simple example that will help you with any problem. We know that the square root of x has an understood index of 2 and power on the x of 1. When we want to convert to a rational exponent the index becomes the denominator and the power becomes the numerator. So sqrt x = x^(1/2)
Another example: sqrt x^3 = x^(3/2)