TEMAT: LICZBY I WYRAŻENIA ALGEBRAICZNE
OBLICZ:
a) (1/3) potęga -1 * (1/3) potęga -2
b) (2/5) potęga -3 : (-2/5) potęga -2
c) ((0,2) potęga -1) potęga -3
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a)3¹*3₂=3*9=27
b)5/2³:-5/2²=125/8*-4/25=-5/2
c)0.2³=0.008
a) (![(\frac{1}{3})^{-1} * (\frac{1}{3})^{-2} = \frac{3}{1} * (\frac{3}{1})^{2} = \frac{3}{1} * \frac{9}{1} = \frac{27}{1} = 27 (\frac{1}{3})^{-1} * (\frac{1}{3})^{-2} = \frac{3}{1} * (\frac{3}{1})^{2} = \frac{3}{1} * \frac{9}{1} = \frac{27}{1} = 27](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B3%7D%29%5E%7B-1%7D+%2A+%28%5Cfrac%7B1%7D%7B3%7D%29%5E%7B-2%7D+%3D+%5Cfrac%7B3%7D%7B1%7D+%2A+%28%5Cfrac%7B3%7D%7B1%7D%29%5E%7B2%7D+%3D+%5Cfrac%7B3%7D%7B1%7D+%2A+%5Cfrac%7B9%7D%7B1%7D+%3D+%5Cfrac%7B27%7D%7B1%7D+%3D+27)
b)![(\frac{2}{5}^{-3} / (-\frac{2}{5})^{-2} = (\frac{5}{2})^{3} / (-\frac{5}{2})^{2} = \frac{125}{8} / \frac {25}{4} = \frac{125}{4} * \frac{4}{25} = \frac{3}{2} = 1\frac{1}{2} (\frac{2}{5}^{-3} / (-\frac{2}{5})^{-2} = (\frac{5}{2})^{3} / (-\frac{5}{2})^{2} = \frac{125}{8} / \frac {25}{4} = \frac{125}{4} * \frac{4}{25} = \frac{3}{2} = 1\frac{1}{2}](https://tex.z-dn.net/?f=%28%5Cfrac%7B2%7D%7B5%7D%5E%7B-3%7D+%2F+%28-%5Cfrac%7B2%7D%7B5%7D%29%5E%7B-2%7D+%3D+%28%5Cfrac%7B5%7D%7B2%7D%29%5E%7B3%7D+%2F+%28-%5Cfrac%7B5%7D%7B2%7D%29%5E%7B2%7D+%3D+%5Cfrac%7B125%7D%7B8%7D+%2F+%5Cfrac+%7B25%7D%7B4%7D+%3D+%5Cfrac%7B125%7D%7B4%7D+%2A+%5Cfrac%7B4%7D%7B25%7D+%3D+%5Cfrac%7B3%7D%7B2%7D+%3D+1%5Cfrac%7B1%7D%7B2%7D)
c)![[(0,2)^{-1}]^{-3} = (0,2)^{3} = 0,8 [(0,2)^{-1}]^{-3} = (0,2)^{3} = 0,8](https://tex.z-dn.net/?f=%5B%280%2C2%29%5E%7B-1%7D%5D%5E%7B-3%7D+%3D+%280%2C2%29%5E%7B3%7D+%3D+0%2C8)