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

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Answer 1 · 2015-10-16T19:12:23

$25sqrt5$

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:

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

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