Question

What is the cube root of x^8?

Answer 1

`root(3)(x^8) = x^2 root(3)(x^2)`

or if you prefer:

`root(3)(x^8) = x^(8/3)`

Explanation:

For any `a, b in RR`, `root(3)(ab) = root(3)(a)root(3)(b)` and `root(3)(a^3) = a`

So:

`root(3)(x^8) = root(3)(x^6 * x^2) = root(3)((x^2)^3*x^2) = root(3)((x^2)^3)root(3)(x^2) = x^2 root(3)(x^2)`