Jak to obliczyć?
1,4 do potęgi 1/4 * 10 do potęgi -1/2
1,4 do potęgi 1/4 * 10 do potęgi -1/2
basetla
![1,4^\frac{1}{4}*10^{-\frac{1}{2}} = 1,4^\frac{1}{4}*(\frac{1}{10})^{\frac{1}{2}} = 1,4^{\frac{1}{4}}*0,1^{\frac{2}{4}} = \sqrt[4]{1,4*0,1^{2}}=\\\\=\sqrt[4]{1,4*0,01}=\sqrt[4]{0,014} \approx0,34](https://tex.z-dn.net/?f=1%2C4%5E%5Cfrac%7B1%7D%7B4%7D%2A10%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D+%3D+1%2C4%5E%5Cfrac%7B1%7D%7B4%7D%2A%28%5Cfrac%7B1%7D%7B10%7D%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D+%3D+1%2C4%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%2A0%2C1%5E%7B%5Cfrac%7B2%7D%7B4%7D%7D+%3D+%5Csqrt%5B4%5D%7B1%2C4%2A0%2C1%5E%7B2%7D%7D%3D%5C%5C%5C%5C%3D%5Csqrt%5B4%5D%7B1%2C4%2A0%2C01%7D%3D%5Csqrt%5B4%5D%7B0%2C014%7D+%5Capprox0%2C34 "1,4^\frac{1}{4}*10^{-\frac{1}{2}} = 1,4^\frac{1}{4}*(\frac{1}{10})^{\frac{1}{2}} = 1,4^{\frac{1}{4}}*0,1^{\frac{2}{4}} = \sqrt[4]{1,4*0,1^{2}}=\\\\=\sqrt[4]{1,4*0,01}=\sqrt[4]{0,014} \approx0,34")
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jestemt
Można na przykład tak :
![(1,4)^{\frac14}*10^{-\frac12} = (\frac{14}{10})^{\frac14}*(\frac{1}{10})^{\frac12} = \frac{14^{\frac14}}{10^{\frac14+\frac12}} = \frac{\sqrt[4]{14}}{10^{\frac34}} = \frac{\sqrt[4]{14}}{\sqrt[4]{10^3}} =\\\\= \sqrt[4]{\frac{14}{1000}} = \sqrt[4]{\frac7{500}}\approx0,34](https://tex.z-dn.net/?f=%281%2C4%29%5E%7B%5Cfrac14%7D%2A10%5E%7B-%5Cfrac12%7D+%3D+%28%5Cfrac%7B14%7D%7B10%7D%29%5E%7B%5Cfrac14%7D%2A%28%5Cfrac%7B1%7D%7B10%7D%29%5E%7B%5Cfrac12%7D+%3D+%5Cfrac%7B14%5E%7B%5Cfrac14%7D%7D%7B10%5E%7B%5Cfrac14%2B%5Cfrac12%7D%7D+%3D+%5Cfrac%7B%5Csqrt%5B4%5D%7B14%7D%7D%7B10%5E%7B%5Cfrac34%7D%7D+%3D+%5Cfrac%7B%5Csqrt%5B4%5D%7B14%7D%7D%7B%5Csqrt%5B4%5D%7B10%5E3%7D%7D+%3D%5C%5C%5C%5C%3D+%5Csqrt%5B4%5D%7B%5Cfrac%7B14%7D%7B1000%7D%7D+%3D+%5Csqrt%5B4%5D%7B%5Cfrac7%7B500%7D%7D%5Capprox0%2C34 "(1,4)^{\frac14}*10^{-\frac12} = (\frac{14}{10})^{\frac14}*(\frac{1}{10})^{\frac12} = \frac{14^{\frac14}}{10^{\frac14+\frac12}} = \frac{\sqrt[4]{14}}{10^{\frac34}} = \frac{\sqrt[4]{14}}{\sqrt[4]{10^3}} =\\\\= \sqrt[4]{\frac{14}{1000}} = \sqrt[4]{\frac7{500}}\approx0,34")
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