Oblicz, a następnie wyznacz odwrotność liczby: [latex] frac{ (-64)^{ frac{1}{3} } * 100^{ frac{3}{2} } }{ (-27)^{ frac{1}{3} } * (-8000)^{ frac{-2}{3} } } [/latex]

[latex]a = frac{(-64)^{frac{1}{3}}*100^{frac{3}{2}}}{(-27)^{frac{1}{3}}*(-8000)^frac{-2}{3}} = frac{sqrt[3]{-64}*(sqrt{100})^3}{sqrt[3]{-27}*(sqrt[3]{-8000})^{-2}} = frac{-4*10^3}{-3*(-20)^{-2}} =\\ frac{-4*1000}{-3*(frac{1}{-20})^2} = frac{-4000}{-3*frac{1}{400}} = frac{-4000}{-frac{3}{400}} = -4000*(-frac{400}{3}) = frac{1600000}{3}\\frac{1}{a} = frac{3}{1600000}[/latex]

[latex]a^{frac{x}{y}}=sqrt[y]{a^{x}}\a^{-x}=(frac{1}{a})^{x} [/latex] [latex]frac{(-64)^{frac{1}{3}}*100^{frac{3}{2}}}{(-27)^{frac{1}{3}}*(-8000)^{-frac{2}{3}}}=frac{sqrt[3]{-64}*sqrt[2]{100^{3}}}{sqrt[3]{-27}*(-frac{1}{8000})^{frac{2}{3}}}=frac{-4*10^{3}}{-3*sqrt[3]{(frac{1}{8000})^{2}}}=frac{-4*1000}{-3*(frac{1}{20})^{2}}=\\frac{-4000}{-3*frac{1}{400}}=frac{-4000}{-frac{3}{400}}=-4000*(-frac{400}{3})=frac{1600000}{3}=533333,(3)\\Odwrotnosc liczby: frac{3}{1600000} [/latex]