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Exponential Representation for Irrational Numbers

Simplify √(√(...

Question

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

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Solution

$\sqrt[4]{\sqrt[3]{x^{2}}} = (x^{2})^{\frac{1}{3}})^{\frac{1}{4}} = (x^{2})^{\frac{1}{3} \times \frac{1}{4}} = (x^{2})^{\frac{1}{12}} = x^{2 \times \frac{1}{12}} = x^{\frac{1}{6}}$

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