Question

How do you simplify `root3(125x^21y^24)`?

Answer 1

`root(3)(125x^21y^24) = 5x^7y^8`

Explanation:

Notice that `(5x^7y^8)^3 = 5^3(x^7)^3(y^8)^3 = 125x^21y^24`

So `5x^7y^8` is a cube root of `125x^21y^24`

Any Real number has a unique Real cube root, so for Real values of `x` and `y` and Real cube roots, we can deduce that this is the cube root we want.