Question

How do you write the radical expression of `4d^(3/8)`?

Answer 1

`4root(8)(d^3)` (or `4(root(8)d)^3`)

Explanation:

The exponent `3/8` applies only to the `d`. (Not to the `4` we are multiplying by.)

An rational exponent `m/n` means take the `n` root, of the `m` power (Or the `m` power of the `n` root.)

So we need the `8` root of the `3` power: `4root(8)(d^3)`

(Or the `3` power of the `8` root: `4(root(8)d)^3`

As long as `m/n` is already reduced to lowest terms, the two expressions are equal:

`root(n)(x^m) = (root(n)x)^m`