Is there a difference if the exponents are fractions or integers?

Answer 1

No. whether or not you use either the radical or fraction depends on personal preference and level of math. In Calculus and higher math solving equations is sometimes easier if you use the fractional powers.

1. x^2 is x squared, (x-a)^3 is (x-a) cubed
2. sqrt(1-x^2)=(1-x^2)^(1/2)

Answer 2

x^2 = x squared
x^5 = x raise to the fifth power
x^1/2 = square root of x
x^1/5 = fifth root of x