Potęgi, logarytmy, funkcja wykładnicza
![a) [ (\frac{2}{3})^-^1 -4^-^1]^-^1= \\ c) 25^{log_5} ^\frac{1}{2}^+ ^\frac{1}{2} * 8^{log_2}^ \sqrt[3]{3} - \frac{1}{3}} \\ d) \sqrt[8]{(3^ \sqrt{3}-1)^ \sqrt{3}+1 }*\sqrt[3]{9} }](https://tex.z-dn.net/?f=a%29+%5B+%28%5Cfrac%7B2%7D%7B3%7D%29%5E-%5E1+-4%5E-%5E1%5D%5E-%5E1%3D+%5C%5C+++c%29+25%5E%7Blog_5%7D+%5E%5Cfrac%7B1%7D%7B2%7D%5E%2B+%5E%5Cfrac%7B1%7D%7B2%7D+%2A+8%5E%7Blog_2%7D%5E+%5Csqrt%5B3%5D%7B3%7D+-+%5Cfrac%7B1%7D%7B3%7D%7D+%5C%5C+++d%29+%5Csqrt%5B8%5D%7B%283%5E+%5Csqrt%7B3%7D-1%29%5E+%5Csqrt%7B3%7D%2B1+%7D%2A%5Csqrt%5B3%5D%7B9%7D+%7D "a) [ (\frac{2}{3})^-^1 -4^-^1]^-^1= \\ c) 25^{log_5} ^\frac{1}{2}^+ ^\frac{1}{2} * 8^{log_2}^ \sqrt[3]{3} - \frac{1}{3}} \\ d) \sqrt[8]{(3^ \sqrt{3}-1)^ \sqrt{3}+1 }*\sqrt[3]{9} }")
Paawełek
![d) \ \sqrt[8]{\left(3^{\sqrt{3}-1}\right)^{\sqrt{3}+1} \cdot \sqrt[3]{9}}=\sqrt[8]{3^{(\sqrt{3}-1)(\sqrt{3}+1)} \cdot \sqrt[8]{9}}=\sqrt[3]{3^{3-1} \cdot \sqrt[3]{9}}=\\ =\sqrt[8]{3^{2}\cdot \sqrt[3]{9}}=\sqrt[8]{9\sqrt[3]{9}}=\sqrt[8]{3^{2} \cdot 3^{\frac{2}{3}}}=\sqrt[8]{3^{2\frac{2}{3}}}=\sqrt[8]{3^{\frac{8}{3}}}= \sqrt[8]{\left(3^{\frac{1}{3}}\right)^{8}}=\\ =3^{\frac{1}{3}}=\sqrt[3]{3}](https://tex.z-dn.net/?f=d%29+%5C+%5Csqrt%5B8%5D%7B%5Cleft%283%5E%7B%5Csqrt%7B3%7D-1%7D%5Cright%29%5E%7B%5Csqrt%7B3%7D%2B1%7D+%5Ccdot+%5Csqrt%5B3%5D%7B9%7D%7D%3D%5Csqrt%5B8%5D%7B3%5E%7B%28%5Csqrt%7B3%7D-1%29%28%5Csqrt%7B3%7D%2B1%29%7D+%5Ccdot+%5Csqrt%5B8%5D%7B9%7D%7D%3D%5Csqrt%5B3%5D%7B3%5E%7B3-1%7D+%5Ccdot+%5Csqrt%5B3%5D%7B9%7D%7D%3D%5C%5C+%3D%5Csqrt%5B8%5D%7B3%5E%7B2%7D%5Ccdot+%5Csqrt%5B3%5D%7B9%7D%7D%3D%5Csqrt%5B8%5D%7B9%5Csqrt%5B3%5D%7B9%7D%7D%3D%5Csqrt%5B8%5D%7B3%5E%7B2%7D+%5Ccdot+3%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%7D%3D%5Csqrt%5B8%5D%7B3%5E%7B2%5Cfrac%7B2%7D%7B3%7D%7D%7D%3D%5Csqrt%5B8%5D%7B3%5E%7B%5Cfrac%7B8%7D%7B3%7D%7D%7D%3D+%5Csqrt%5B8%5D%7B%5Cleft%283%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%5Cright%29%5E%7B8%7D%7D%3D%5C%5C+%3D3%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%3D%5Csqrt%5B3%5D%7B3%7D+ "d) \ \sqrt[8]{\left(3^{\sqrt{3}-1}\right)^{\sqrt{3}+1} \cdot \sqrt[3]{9}}=\sqrt[8]{3^{(\sqrt{3}-1)(\sqrt{3}+1)} \cdot \sqrt[8]{9}}=\sqrt[3]{3^{3-1} \cdot \sqrt[3]{9}}=\\ =\sqrt[8]{3^{2}\cdot \sqrt[3]{9}}=\sqrt[8]{9\sqrt[3]{9}}=\sqrt[8]{3^{2} \cdot 3^{\frac{2}{3}}}=\sqrt[8]{3^{2\frac{2}{3}}}=\sqrt[8]{3^{\frac{8}{3}}}= \sqrt[8]{\left(3^{\frac{1}{3}}\right)^{8}}=\\ =3^{\frac{1}{3}}=\sqrt[3]{3}")
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