Expresa mediante un solo radical
A) ![\sqrt \frac{ \sqrt{2} }{ \sqrt[3]2}](https://tex.z-dn.net/?f=+%5Csqrt++%5Cfrac%7B+%5Csqrt%7B2%7D+%7D%7B+%5Csqrt%5B3%5D2%7D "\sqrt \frac{ \sqrt{2} }{ \sqrt[3]2}")
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Aplicando las convenientes propiedades operatorias de potencias y raices
![\sqrt{ \frac{ \sqrt{2} }{ \sqrt[3]{2} } } \\ \\ = \sqrt{ \frac{ 2^{ \frac{1}{2} } }{ 2^{ \frac{1}{3} } } } \\ \\ = \sqrt{ 2^{ \frac{1}{2}- \frac{1}{3} } } \\ \\= \sqrt{ 2^{ \frac{1}{6} } } \\ \\ = (2^{ \frac{1}{6} } ) ^{ \frac{1}{2} } \\ \\ = 2^{ \frac{1}{6}x \frac{1}{2} } \\ \\ = 2^{ \frac{1}{12} }](https://tex.z-dn.net/?f=+%5Csqrt%7B+%5Cfrac%7B+%5Csqrt%7B2%7D+%7D%7B+%5Csqrt%5B3%5D%7B2%7D+%7D+%7D++%5C%5C++%5C%5C+%3D+%5Csqrt%7B+%5Cfrac%7B+2%5E%7B+%5Cfrac%7B1%7D%7B2%7D+%7D+%7D%7B+2%5E%7B+%5Cfrac%7B1%7D%7B3%7D+%7D+%7D+%7D++%5C%5C++%5C%5C+%3D+%5Csqrt%7B+2%5E%7B+%5Cfrac%7B1%7D%7B2%7D-+%5Cfrac%7B1%7D%7B3%7D++%7D+%7D++%5C%5C++%5C%5C%3D++%5Csqrt%7B+2%5E%7B+%5Cfrac%7B1%7D%7B6%7D+%7D+%7D++%5C%5C++%5C%5C+%3D+%282%5E%7B+%5Cfrac%7B1%7D%7B6%7D+%7D+%29+%5E%7B+%5Cfrac%7B1%7D%7B2%7D+%7D++%5C%5C++%5C%5C+%3D+2%5E%7B+%5Cfrac%7B1%7D%7B6%7Dx+%5Cfrac%7B1%7D%7B2%7D++%7D++%5C%5C++%5C%5C+%3D+2%5E%7B+%5Cfrac%7B1%7D%7B12%7D+%7D+ "\sqrt{ \frac{ \sqrt{2} }{ \sqrt[3]{2} } } \\ \\ = \sqrt{ \frac{ 2^{ \frac{1}{2} } }{ 2^{ \frac{1}{3} } } } \\ \\ = \sqrt{ 2^{ \frac{1}{2}- \frac{1}{3} } } \\ \\= \sqrt{ 2^{ \frac{1}{6} } } \\ \\ = (2^{ \frac{1}{6} } ) ^{ \frac{1}{2} } \\ \\ = 2^{ \frac{1}{6}x \frac{1}{2} } \\ \\ = 2^{ \frac{1}{12} }")
![= \sqrt[12]{2}](https://tex.z-dn.net/?f=%3D+%5Csqrt%5B12%5D%7B2%7D+ "= \sqrt[12]{2}")
RESULTADO FINAL
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