Question

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

Answer 1

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!