[tex]a) \ 3^{3} = 3\cdot3\cdot3 = 27\\\\b) \ (\frac{2}{5})^{-2} = (\frac{5}{2})^{2} =\frac{25}{4} = 6\frac{1}{4}\\\\c) \ (2^{-4}:2^{-6})^{-1} = (2^{-4-(-6)})^{-1} = (2^{2})^{-1} = 2^{-2} = (\frac{1}{2})^{2} = \frac{1}{4}\\\\d) \ 49^{1,5} = (7^{2})^{\frac{3}{2}} = 7^{3} = 343[/tex]
[tex]e) \ (\frac{2}{5})^{-3}:(\frac{125}{8})^{\frac{1}{6}} = (\frac{5}{2})^{3}:((\frac{5}{2})^{3})^{\frac{1}{6}} = (\frac{5}{2})^{3}:(\frac{5}{2})^{\frac{1}{2}} =(\frac{5}{2})^{2\frac{1}{2}} = (\frac{5}{2})^{2}\cdot(\frac{5}{2})^{\frac{1}{2}} = \frac{25}{4}\sqrt{\frac{5}{2}}[/tex]
Wyjaśnienie:
[tex]a^{m}:a^{n} = a^{m-n}\\(a^{m})^{n} = a^{m\cdot n}\\(\frac{a}{b})^{-n}=(\frac{b}{a})^{n}[/tex]