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Step-by-step explanation:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[
\sqrt[3]{\frac{a}{b}}\qquad \sqrt[\leftroot{-1}\uproot{2}\scriptstyle 3]{\frac{a}{b}}\qquad
\Bigl(\frac{a}{b}\Bigr)^{1/3}
\]
\end{document}
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