How can an expression written in either radical form or rational exponent form be rewritten to fit the other form?

When dealing with radicals and exponents, one must realize that fractional exponents deals directly with radicals. In that sense, sqrt(x) = x^1/2
Now, how to go about doing this: 

In a fractional exponent, the numerator represents the actual exponent of the number. So, for x^2/3, the x is being squared. 

For the denominator, that deals with the radical. The index, to be exact. The index describes what KIND of radical (or root) is being taken: square, cube, fourth, fifth, and so on. So, for our example x^2/3, x is squared, and that quantity is under a cube root (or a radical with a 3). Here are some more examples to help you understand a bit more:
x^6/5 = Fifth root of x^6
x^3/1 = x^3
^^^Exponential fractions still follow the same rules of simplifying, so...
x^2/4 = x^1/2 = sqrt(x)

Hope this helps!