Question 43251
Okay, here is what I would say...
Using rational exponents is a clearer, cleaner and more condensed way to express all roots in general. Using radical signs is rather clumsy, especially when you wish to combine different roots.  Thus rational exponents has a clear advantage in this regard.
An example equation might be
x^(2/3) * x^(1/5) + 1 = 3
Here you can merely add the exponents together, whereas if you expressed these as roots within radical signs, you would be forced to change everything to fifteenth roots first, etc., thereby introducing a greater chance of misunderstanding and subsequent error.
To finish the problem, we get
x^(13/15) = 2
x = 2^(15/13)
How does that work for you?