[tex]zad.1\\\\(-2,56)^{3} \div (\frac{16}{25} )^{3} =(-2\frac{56}{100}) ^{3} \div (\frac{16}{25} )^{3}=(-\frac{256}{100} )^{3} \div (\frac{16}{25} )^{3} = ( -\frac{256}{100} \div \frac{16}{25}) ^{3} =( -\frac{256}{100} \cdot \frac{25}{16}) ^{3} =( - \frac{16}{4} )^{3} =(-4)^{3} = - 64\\\\zad.2\\\\(-0,9)^{2} \div (\frac{3}{8}) ^{2} =(0,9)^{2} \div (\frac{3}{8}) ^{2}=(\frac{9}{10} )^{2} \div (\frac{3}{8}) ^{2}=(\frac{9}{10}\div \frac{3}{8} ) ^{2} =(\frac{9}{10}\cdot \frac{8}{3} ) ^{2} =[/tex]
[tex]= (\frac{3\cdot 4}{5} )^{2} =(\frac{12}{5} )^{2} =\frac{144}{25} =5\frac{19}{25} =5\frac{76}{100} =5,76[/tex]
[tex]zad.3\\\\(1\frac{2}{3} )^{4} \div (-2\frac{7}{9} )^{4} =(1\frac{2}{3} )^{4} \div (2\frac{7}{9} )^{4}=(\frac{5}{3} )^{4} \div (\frac{25}{9} )^{4}=(\frac{5}{3} \div\frac{25}{9} ) ^{4} =(\frac{5}{3} \cdot \frac{9}{25} ) ^{4}=(\frac{3}{5} )^{4} =\frac{81}{625}[/tex]
Korzystałam z następujących wzorów:
[tex]x^{n} \div y^{n} =(x\div y)^{n} =(\frac{x}{y} )^{n} \\\\(-x)^{n} = x^{n} ~~gdy~~n~~jest~~parzyste\\\\(-x)^{n} =- x^{n} ~~gdy~~n~~jest~~nieparzyste\\ \\(\frac{x}{y} )^{n} \div (\frac{a}{b}) ^{n} =(\frac{x}{y}\div \frac{a}{b})^{n}=(\frac{x}{y}\cdot \frac{b}{a})^{n}[/tex]
