Question

Simplify the expression ${\left(5^{\sqrt{2}}\right)}^{\sqrt{8}}$.

Short answer

The simplified value of expression is625.

Step-by-step solution

Step 1. Write down the given expression.

The given expression is ${\left(5^{\sqrt{2}}\right)}^{\sqrt{8}}$.

Step 2. Simplify the expression.

The given expression ${\left(5^{\sqrt{2}}\right)}^{\sqrt{8}}$is simplified as:

$\begin{array}{l}{\left(5^{\sqrt{2}}\right)}^{\sqrt{8}}={\left(5\right)}^{\sqrt{2}\times \sqrt{8}}\\ ={\left(5\right)}^{\sqrt{16}}\\ ={\left(5\right)}^4\\ =625\end{array}$

Step 3. Conclusion.

The simplified value of expression is $625$.