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- We know that
- (2/10)⁷ = 128/10000000
So seventh root of 0.0000128 = 2/10
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![\sqrt[7]{0.0000128} \\ \\ = {(0.0000128)}^{ \frac{1}{7} } \\ \\ = ({ \frac{128}{10000000}) }^{ \frac{1}{7} } \\ \\ = ({ \frac{ {2}^{7} }{ {10}^{7} }) }^{ \frac{1}{7} } \\ \\ = { ({ \frac{2}{10} }^{7}) }^{ \frac{1}{7} } \\ \\ = \frac{2}{10} \\ \\ = 0.2](https://tex.z-dn.net/?f=+%5Csqrt%5B7%5D%7B0.0000128%7D++%5C%5C++%5C%5C++%3D++%7B%280.0000128%29%7D%5E%7B+%5Cfrac%7B1%7D%7B7%7D+%7D++%5C%5C++%5C%5C++%3D+++%28%7B+%5Cfrac%7B128%7D%7B10000000%7D%29+%7D%5E%7B+%5Cfrac%7B1%7D%7B7%7D+%7D++%5C%5C++%5C%5C++%3D++%28%7B+%5Cfrac%7B+%7B2%7D%5E%7B7%7D+%7D%7B+%7B10%7D%5E%7B7%7D+%7D%29+%7D%5E%7B+%5Cfrac%7B1%7D%7B7%7D+%7D++%5C%5C++%5C%5C++%3D++%7B+%28%7B+%5Cfrac%7B2%7D%7B10%7D+%7D%5E%7B7%7D%29+%7D%5E%7B+%5Cfrac%7B1%7D%7B7%7D+%7D++%5C%5C++%5C%5C++%3D++%5Cfrac%7B2%7D%7B10%7D++%5C%5C++%5C%5C++%3D+0.2 "\sqrt[7]{0.0000128} \\ \\ = {(0.0000128)}^{ \frac{1}{7} } \\ \\ = ({ \frac{128}{10000000}) }^{ \frac{1}{7} } \\ \\ = ({ \frac{ {2}^{7} }{ {10}^{7} }) }^{ \frac{1}{7} } \\ \\ = { ({ \frac{2}{10} }^{7}) }^{ \frac{1}{7} } \\ \\ = \frac{2}{10} \\ \\ = 0.2")
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