Działania na potęgach. Proszę o rozwiązanie i wytłumaczenie
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1)![\frac{3x-2- \sqrt[3]{x} }{2x \sqrt[4]{x} }](https://tex.z-dn.net/?f=+%5Cfrac%7B3x-2-+%5Csqrt%5B3%5D%7Bx%7D+%7D%7B2x+%5Csqrt%5B4%5D%7Bx%7D+%7D+ "\frac{3x-2- \sqrt[3]{x} }{2x \sqrt[4]{x} }")
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3)![\frac{ x^{2}- \sqrt{x} + \sqrt[3]{x} }{ \sqrt{3x} }](https://tex.z-dn.net/?f=+%5Cfrac%7B+x%5E%7B2%7D-+%5Csqrt%7Bx%7D+%2B+%5Csqrt%5B3%5D%7Bx%7D+%7D%7B+%5Csqrt%7B3x%7D+%7D+ "\frac{ x^{2}- \sqrt{x} + \sqrt[3]{x} }{ \sqrt{3x} }")
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jestemt
![1)\ \frac{3x-2-\sqrt[3]x}{2x\sqrt[4]x} = \frac{3x}{2x^{1+\frac14}}-\frac{2}{2x^{1+\frac14}}-\frac{x^{\frac13}}{2x^{1+\frac14}} = \\\\=\frac32*x^{1-1-\frac14}-1x^{0-1-\frac14}-\frac12x^{\frac13-1-\frac14} = 1,5x^{-\frac14}-1x^{-\frac54}-\frac12x^{-\frac23-\frac14} = \\\\=1,5x^{-\frac14}+(-1)x^{-\frac54}+(-\frac12)x^{-\frac{11}{12}}\\\\\\2)\ \frac{(x+7)^3}{3x^2} = \frac{x^3+21x^2+147x+343}{3x^2} = \frac13x+7x^0+49x^{-1}+114\frac13*x^{-2}](https://tex.z-dn.net/?f=1%29%5C+%5Cfrac%7B3x-2-%5Csqrt%5B3%5Dx%7D%7B2x%5Csqrt%5B4%5Dx%7D+%3D+%5Cfrac%7B3x%7D%7B2x%5E%7B1%2B%5Cfrac14%7D%7D-%5Cfrac%7B2%7D%7B2x%5E%7B1%2B%5Cfrac14%7D%7D-%5Cfrac%7Bx%5E%7B%5Cfrac13%7D%7D%7B2x%5E%7B1%2B%5Cfrac14%7D%7D+%3D+%5C%5C%5C%5C%3D%5Cfrac32%2Ax%5E%7B1-1-%5Cfrac14%7D-1x%5E%7B0-1-%5Cfrac14%7D-%5Cfrac12x%5E%7B%5Cfrac13-1-%5Cfrac14%7D+%3D+1%2C5x%5E%7B-%5Cfrac14%7D-1x%5E%7B-%5Cfrac54%7D-%5Cfrac12x%5E%7B-%5Cfrac23-%5Cfrac14%7D+%3D+%5C%5C%5C%5C%3D1%2C5x%5E%7B-%5Cfrac14%7D%2B%28-1%29x%5E%7B-%5Cfrac54%7D%2B%28-%5Cfrac12%29x%5E%7B-%5Cfrac%7B11%7D%7B12%7D%7D%5C%5C%5C%5C%5C%5C2%29%5C+%5Cfrac%7B%28x%2B7%29%5E3%7D%7B3x%5E2%7D+%3D+%5Cfrac%7Bx%5E3%2B21x%5E2%2B147x%2B343%7D%7B3x%5E2%7D+%3D+%5Cfrac13x%2B7x%5E0%2B49x%5E%7B-1%7D%2B114%5Cfrac13%2Ax%5E%7B-2%7D "1)\ \frac{3x-2-\sqrt[3]x}{2x\sqrt[4]x} = \frac{3x}{2x^{1+\frac14}}-\frac{2}{2x^{1+\frac14}}-\frac{x^{\frac13}}{2x^{1+\frac14}} = \\\\=\frac32*x^{1-1-\frac14}-1x^{0-1-\frac14}-\frac12x^{\frac13-1-\frac14} = 1,5x^{-\frac14}-1x^{-\frac54}-\frac12x^{-\frac23-\frac14} = \\\\=1,5x^{-\frac14}+(-1)x^{-\frac54}+(-\frac12)x^{-\frac{11}{12}}\\\\\\2)\ \frac{(x+7)^3}{3x^2} = \frac{x^3+21x^2+147x+343}{3x^2} = \frac13x+7x^0+49x^{-1}+114\frac13*x^{-2}")
![\\\\\\3)\ \frac{x^2-\sqrt{x}+\sqrt[3]x}{\sqrt{3x}} = \frac{x^2}{3^{0,5}*x^{0,5}}-\frac{x^{0,5}}{3^{0,5}x^{0,5}}+\frac{x^{\frac13}}{3^{0,5}x^{\frac12}} =\\\\= \frac{1}{\sqrt3}*x^{2-0,5}-\frac1{\sqrt3}}*x^{0,5-0,5}+\frac1{\sqrt3}x^{\frac13-\frac12} = \\\\\frac{\sqrt3}{3}x^{\frac32}-\frac{\sqrt3}{3}x^0+\frac{\sqrt3}{3}*x^{\frac26-\frac36} = \frac{\sqrt3}{3}x^{\frac32}+(-\frac{\sqrt3}3)x^0+\frac{\sqrt3}3x^{-\frac16}](https://tex.z-dn.net/?f=%5C%5C%5C%5C%5C%5C3%29%5C+%5Cfrac%7Bx%5E2-%5Csqrt%7Bx%7D%2B%5Csqrt%5B3%5Dx%7D%7B%5Csqrt%7B3x%7D%7D+%3D+%5Cfrac%7Bx%5E2%7D%7B3%5E%7B0%2C5%7D%2Ax%5E%7B0%2C5%7D%7D-%5Cfrac%7Bx%5E%7B0%2C5%7D%7D%7B3%5E%7B0%2C5%7Dx%5E%7B0%2C5%7D%7D%2B%5Cfrac%7Bx%5E%7B%5Cfrac13%7D%7D%7B3%5E%7B0%2C5%7Dx%5E%7B%5Cfrac12%7D%7D+%3D%5C%5C%5C%5C%3D+%5Cfrac%7B1%7D%7B%5Csqrt3%7D%2Ax%5E%7B2-0%2C5%7D-%5Cfrac1%7B%5Csqrt3%7D%7D%2Ax%5E%7B0%2C5-0%2C5%7D%2B%5Cfrac1%7B%5Csqrt3%7Dx%5E%7B%5Cfrac13-%5Cfrac12%7D+%3D+%5C%5C%5C%5C%5Cfrac%7B%5Csqrt3%7D%7B3%7Dx%5E%7B%5Cfrac32%7D-%5Cfrac%7B%5Csqrt3%7D%7B3%7Dx%5E0%2B%5Cfrac%7B%5Csqrt3%7D%7B3%7D%2Ax%5E%7B%5Cfrac26-%5Cfrac36%7D+%3D+%5Cfrac%7B%5Csqrt3%7D%7B3%7Dx%5E%7B%5Cfrac32%7D%2B%28-%5Cfrac%7B%5Csqrt3%7D3%29x%5E0%2B%5Cfrac%7B%5Csqrt3%7D3x%5E%7B-%5Cfrac16%7D "\\\\\\3)\ \frac{x^2-\sqrt{x}+\sqrt[3]x}{\sqrt{3x}} = \frac{x^2}{3^{0,5}*x^{0,5}}-\frac{x^{0,5}}{3^{0,5}x^{0,5}}+\frac{x^{\frac13}}{3^{0,5}x^{\frac12}} =\\\\= \frac{1}{\sqrt3}*x^{2-0,5}-\frac1{\sqrt3}}*x^{0,5-0,5}+\frac1{\sqrt3}x^{\frac13-\frac12} = \\\\\frac{\sqrt3}{3}x^{\frac32}-\frac{\sqrt3}{3}x^0+\frac{\sqrt3}{3}*x^{\frac26-\frac36} = \frac{\sqrt3}{3}x^{\frac32}+(-\frac{\sqrt3}3)x^0+\frac{\sqrt3}3x^{-\frac16}")
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