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