[latex] \sqrt[6]{ \sqrt \alpha ^{3} } [/latex]

[latex]\sqrt[6]{\sqrt{\alpha ^{3}}}=\left ( \left ( \alpha ^ {3} \right )^{\frac{1}{2}} \right )^\frac{1}{6}=\\ =\left ( \left ( \left ( \alpha ^3 \right )^{\frac{1}{3}} \right )^{\frac{1}{2}} \right )^{\frac{1}{2}}=\left ( \alpha ^{\frac{1}{2}} \right )^{\frac{1}{2}}=\\ =\alpha ^{\frac{1}{4}}=\sqrt[4]{\alpha }[/latex]