Question

What is the simplified radical form of `(5)^(5/2)`?

Answer 1

`25sqrt5`

Explanation:

Keep this rule in mind:

`color(white)(XX)a^(m/n)=root(n)(a^m)`

Now that you know that rule, you can convert it to radical form.

`color(white)(XX)5^(5/2)=sqrt(5^5)`

We can simplify this further:

`sqrt(5^5)=sqrt(5^4*5)=5^2sqrt5=color(red)(25sqrt5)`