Simplify
Question:

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

Solution:

$\sqrt[4]{\sqrt[3]{x^{2}}}=\left[\left(x^{2}\right)^{\frac{1}{3}}\right]^{\frac{1}{4}}$

$=\left[x^{\frac{2}{3}}\right]^{\frac{1}{4}}$

$=x^{\frac{2}{12}}$

$=x^{\frac{1}{6}}$

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