Simplify $\sqrt[4]{\sqrt[3]{x^2}}$ and express the result in the exponential form of x.

$$\begin{gathered} \sqrt[4]{\sqrt[3]{x^2}}={\left[{\left(x^2\right)}^{\frac{1}{3}}\right]}^{\frac{1}{4}} \\ ={\left[x^{\frac{2}{3}}\right]}^{\frac{1}{4}} \\ =x^{\frac{2}{12}} \\ =x^{\frac{1}{6}} \end{gathered}$$

Hence, the result in the exponential form is $x^{\frac{1}{6}}$.