Question

How do you write `root5(2^8)` as a radical?

Answer 1

See a solution process below:

Explanation:

This is already written as a radical. However, we can simplify this term by rewriting the term under the radical and then using this rule of radicals:

`root(n)(color(red)(a)) * root(n)(color(blue)(b)) = root(n)(color(red)(a) * color(blue)(b))`

`root(5)(2^8) => root(5)(color(red)(2^5) * color(blue)(2^3)) = root(5)(color(red)(2^5)) * root(5)(color(blue)(2^3)) => 2root(5)(color(blue)(2^3))`

If necessary, this can be rewritten as:

`2root(5)(8)`