OBLICZ
1.[tex](2\frac{1}{8} - 3\frac{1}{2}):1\frac{1}{6} + 0,3[/tex]
2.·[tex](3-4 razy 2x^{-2})^{-3}[/tex]
3.[tex](3a-1)^{2} - (1+3a)^{2}[/tex]
4.[tex]16^{ -\frac{2}{3} } razy (0,2)^{-1} + 81^{\frac{3}{4}} razy 27^{-\frac{2}{3} }[/tex] tu sa nie ułamki tylko do potegi liczby
1.[tex](2\frac{1}{8} - 3\frac{1}{2}):1\frac{1}{6} + 0,3[/tex]
2.·[tex](3-4 razy 2x^{-2})^{-3}[/tex]
3.[tex](3a-1)^{2} - (1+3a)^{2}[/tex]
4.[tex]16^{ -\frac{2}{3} } razy (0,2)^{-1} + 81^{\frac{3}{4}} razy 27^{-\frac{2}{3} }[/tex] tu sa nie ułamki tylko do potegi liczby
Odpowiedź:
1. [tex](2\frac{1}{8} - 3\frac{1}{2}) / 1\frac{1}{6} + 0,3 = (\frac{17}{8} - \frac{7}{2}) / \frac{7}{6} + \frac{3}{10} = (\frac{17}{8} - \frac{28}{8}) / \frac{7}{6} + \frac{3}{10} = (-\frac{11}{8}) * \frac{6}{7} + \frac{3}{10} =[/tex]
[tex]- \frac{66}{56} + \frac{3}{10} = -\frac{330}{280} + \frac{84}{280} = - \frac{246}{280} = - \frac{123}{140}[/tex]
2. [tex](3 - 4 * 2x^{-2})^{-3} = (3 - 8x^{-2})^{-3} = (\frac{1}{9} - {\frac{8}{x^{2}})^{-3} = 729 - \frac{x^{5}}{512}[/tex]
3. (3a - 1)² - (1 + 3a)² = 9a² - 6a + 1 - 1 - 6a - 9a² = 0
4. [tex]16^{-\frac{2}{3}} * (0,2)^{-1} + 81^{\frac{3}{4}} * 27^{-\frac{2}{3}} = \sqrt[3]{\frac{1}{16}^{2}} * 5 + \sqrt[4]{81^{3}} * \sqrt[3]{\frac{1}{27}^{2}} =[/tex]
[tex]= 5\sqrt[3]{\frac{1}{256}} + \sqrt[4]{(3^{4})^{3}}} * \sqrt[3]{((\frac{1}{3})^{3})^{2}} = 5\sqrt[3]{\frac{1}{256}} + 3^{3} * (\frac{1}{3})^{2} =5\sqrt[3]{\frac{1}{256}} + 3^{3} * 3^{-2} =[/tex]
[tex]=5\sqrt[3]{\frac{1}{256}} + 3[/tex]