Question

22 지
$\sqrt{2 \sqrt[3]{2} } \div \sqrt[3]{2} \sqrt{2} =$
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Answer 1

$\frac{\sqrt{2\sqrt[3]{2} }}{\sqrt[3]{2}\cdot \sqrt{2} }= \frac{(2\cdot 2^{\frac{1}{3}})^\frac{1}{2}}{2^\frac{1}{3}\cdot 2^\frac{1}{2}}=\frac{(2^\frac{4}{3})^\frac{1}{2}}{2^\frac{5}{6}}=\frac{2^\frac{2}{3}}{2^\frac{5}{6}}=2^{(\frac{2}{3}-\frac{5}{6})}=2^{-\frac{1}{6}}=\frac{1}{\sqrt[6]{2} }$