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Laws of Surds

\begin{aligned}
i.) & \sqrt[n]{a} = a^{\frac{1}{n}} \\
ii.) & \sqrt[n]{ab} = \sqrt[n]{a} * \sqrt[n]{b} \\
iii.) & \sqrt[n]{\frac{a}{b}} = \frac{\sqrt[n]{a}}{ \sqrt[n]{b}} \\

iv.)& (\sqrt[n]{a})^n = a \\

v.)& (\sqrt[m]{\sqrt[n]{a}}) = \sqrt[mn]{a} \\

vi.)& (\sqrt[n]{a})^m = \sqrt[n]{a^m}
\end{aligned}