To express [tex]\((20)^{\frac{5}{2}}\)[/tex] in its simplest radical form, let's break down the process step by step.
1. Understand the Exponent: [tex]\(\frac{5}{2}\)[/tex] signifies that we will raise 20 to the 5th power and then take the square root of the result (or vice versa).
2. Rewrite with Radicals:
[tex]\[
(20)^{\frac{5}{2}} = \sqrt{(20)^5}
\][/tex]
3. Express the Radical: We can write the expression inside the radical fully.
[tex]\[
\sqrt{(20)^5}
\][/tex]
Therefore, the radical form of [tex]\((20)^{\frac{5}{2}}\)[/tex] is [tex]\(\sqrt{20^5}\)[/tex].
In simplest radical form:
[tex]\[
\boxed{\sqrt{(20)^5}}
\][/tex]
