[tex]4^{-\frac{1}{2} } =(\dfrac{1}{4} )^{\frac{1}{2} } =\sqrt[2]{\dfrac{1}{4} } =\sqrt[2]{\dfrac{1^{2} }{2^{2} } }=\dfrac{1}{2} \\\\\\0,125^{-\frac{2}{3} } =(\dfrac{125}{1000} )^{-\frac{2}{3} }=(\dfrac{1}{8} )^{-\frac{2}{3} }=(\dfrac{8}{1} )^{\frac{2}{3} }=(2^{3} )^{\frac{2}{3} }=2^{3\cdot \frac{2}{3} } =2^{2} =4\\\\[/tex]
[tex]0,36^{-\frac{3}{2} } =(\dfrac{36}{100} )^{-\frac{3}{2} }=(\dfrac{100}{36} )^{\frac{3}{2} }=((\frac{10}{6} )^{2} )^{\frac{3}{2} }=(\frac{5}{3} )^{2\cdot \frac{3}{2} }=(\dfrac{5}{3} )^{3} =\dfrac{125}{27} =4\dfrac{17}{27} \\\\\\625^{-0,75} =625^{-\frac{3}{4} } =(\dfrac{1}{625} )^{\frac{3}{4} } =((\dfrac{1}{5} )^{4} )^{\frac{3}{4} } =(\dfrac{1}{5} )^{4\cdot \frac{3}{4} } =(\dfrac{1}{5} )^{3 } =\dfrac{1}{125}[/tex]
[tex]0,16^{-2,5} =(\frac{16}{100} )^{-2\frac{1}{2} } =(\frac{16}{100} )^{-\frac{5}{2} }=(\frac{100}{16} )^{\frac{5}{2} }=((\frac{10}{4} )^{2} )^{\frac{5}{2} } =((\frac{5}{2} )^{2} )^{\frac{5}{2} } =(\frac{5}{2} )^{2\cdot \frac{5}{2} } =(\frac{5}{2} )^{5 } =\dfrac{3125}{32} =97\dfrac{21}{32}[/tex]
korzystam ze wzorów:
[tex]x^{-n} =(\dfrac{1}{x} )^{n} \\\\a^{\frac{x}{y} } =\sqrt[y]{a^{x} } \\\\(x^{n} )^{m} =x^{n\cdot m} \\\\\sqrt[n]{x^{n} } =x[/tex]
