Simplify the Nested Radical: Fifth Root of Square Root of x^20

Complete the following exercise:

$\sqrt[5]{\sqrt{x^{20}}}=$

To solve the problem $\sqrt[5]{\sqrt{x^{20}}}$, we will convert the roots into fractional exponents and simplify:

The expression $\sqrt{x^{20}}$ can be represented as:

$(x^{20})^{\frac{1}{2}} = x^{20 \cdot \frac{1}{2}} = x^{10}$

Now, taking the fifth root of $x^{10}$, we have:

$(x^{10})^{\frac{1}{5}} = x^{10 \cdot \frac{1}{5}} = x^{2}$

Therefore, the original expression $\sqrt[5]{\sqrt{x^{20}}}$ simplifies to $x^2$.