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2![2^{1 \frac{1}{2} } : \sqrt[3]{ \frac{1}{ 2^{2} } }](https://tex.z-dn.net/?f=+2%5E%7B1+%5Cfrac%7B1%7D%7B2%7D+%7D+%3A+%5Csqrt%5B3%5D%7B+%5Cfrac%7B1%7D%7B+2%5E%7B2%7D+%7D+%7D+ "2^{1 \frac{1}{2} } : \sqrt[3]{ \frac{1}{ 2^{2} } }")
adalah...
a.
b.![\sqrt[6]{2}](https://tex.z-dn.net/?f=+%5Csqrt%5B6%5D%7B2%7D+ "\sqrt[6]{2}")
c.![4 \sqrt[6]{2}](https://tex.z-dn.net/?f=4+%5Csqrt%5B6%5D%7B2%7D+ "4 \sqrt[6]{2}")
d.![4 \sqrt[4]{2}](https://tex.z-dn.net/?f=4+%5Csqrt%5B4%5D%7B2%7D+ "4 \sqrt[4]{2}")
2
adalah...
a.
b.
c.
d.
Takamori37
![$\begin{align}2^{1\frac{1}{2}}:\sqrt[3]{\frac{1}{2^2}}&=2^{\frac{3}{2}}:\sqrt[3]{2^{-2}} \\ &=2^{3/2}:2^{-2/3} \\ &=2^{\frac{3}{2}-(-\frac{2}{3})} \\ &=2^{(9+4)/6} \\ &=2^{13/6} \\ &=2^2\times 2^{1/6} \\ &=4\sqrt[6]{2}\end{align}](https://tex.z-dn.net/?f=%24%5Cbegin%7Balign%7D2%5E%7B1%5Cfrac%7B1%7D%7B2%7D%7D%3A%5Csqrt%5B3%5D%7B%5Cfrac%7B1%7D%7B2%5E2%7D%7D%26%3D2%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%3A%5Csqrt%5B3%5D%7B2%5E%7B-2%7D%7D+%5C%5C+%26%3D2%5E%7B3%2F2%7D%3A2%5E%7B-2%2F3%7D+%5C%5C+%26%3D2%5E%7B%5Cfrac%7B3%7D%7B2%7D-%28-%5Cfrac%7B2%7D%7B3%7D%29%7D+%5C%5C+%26%3D2%5E%7B%289%2B4%29%2F6%7D+%5C%5C+%26%3D2%5E%7B13%2F6%7D+%5C%5C+%26%3D2%5E2%5Ctimes+2%5E%7B1%2F6%7D+%5C%5C+%26%3D4%5Csqrt%5B6%5D%7B2%7D%5Cend%7Balign%7D "$\begin{align}2^{1\frac{1}{2}}:\sqrt[3]{\frac{1}{2^2}}&=2^{\frac{3}{2}}:\sqrt[3]{2^{-2}} \\ &=2^{3/2}:2^{-2/3} \\ &=2^{\frac{3}{2}-(-\frac{2}{3})} \\ &=2^{(9+4)/6} \\ &=2^{13/6} \\ &=2^2\times 2^{1/6} \\ &=4\sqrt[6]{2}\end{align}")
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