Solving equations involving fractional exponents?

Question

Let's say we have the following equation (with $a,b \in \mathbb{Z}$): $$x^\frac{a}{b} = 2$$

If the exponent is an even integer, we get two solutions. If it is an odd integer, we get only one solution. How about the other cases and how do I write the result in closed form?

Answer 1

Then do $$\left (x^{a/b}\right )^b=2^b,$$ gives you the equation $x^a=2^b.$ This one you know how to solve.