Question

How do you simplify `root7(640 )`?

Answer 1

`root(7)(640) = 2root(7)(5)`

Explanation:

There are a couple of properties that hold for any `n`th root (where `n` is a positive integer), including `7`th roots:

`root(n)(ab) = root(n)(a)root(n)(b)" "` when `a, b >= 0`

`root(n)(a^n) = a" "` when `a >= 0`

Factorising `640`, we find:

`640 = 2^7*5`

So:

`root(7)(640) = root(7)(2^7*5) = root(7)(2^7)*root(7)(5) = 2root(7)(5)`