[tex](\dfrac{2}{5} )^{5} \cdot (6\dfrac{1}{4} )^{3} =(\dfrac{2}{5} )^{5} \cdot (\dfrac{25}{4} )^{3}=(\dfrac{2}{5} )^{5} \cdot [(\dfrac{5}{2} )^{2} ]^{3}=(\dfrac{2}{5} )^{5} \cdot (\dfrac{5}{2} )^{2\cdot 3}=(\dfrac{2}{5} )^{5} \cdot (\dfrac{5}{2} )^{6} =(\dfrac{2}{5} )^{5} \cdot (\dfrac{2}{5} )^{-6} =(\dfrac{2}{5} )^{5+(-6)} =(\dfrac{2}{5} )^{5-6}=(\dfrac{2}{5} )^{-1} =(\dfrac{5}{2} )^{1} =\dfrac{5}{2}=2\dfrac{1}{2} =2,5[/tex]
korzystałam ze wzorów:
[tex](x^{n} )^{m} =x^{n\cdot m} \\\\x^{-n} =(\frac{1}{x} )^{n} \\\\x^{n} \cdot x^{m} =x^{n+m}[/tex]
