[tex]zad.5\\\\a)\\\\\sqrt[5]{4^{2\frac{1}{2} } }= \sqrt[5]{4^{\frac{5}{2} } }=(4^{\frac{5}{2} })^{\frac{1}{5} } =4^{\frac{5}{2}\cdot \frac{1}{5} }=4^{\frac{1}{2} }=(2^{2} )^{\frac{1}{2} }=2^{2\cdot \frac{1}{2} } =2^{1} =2\\\\b)\\\\\sqrt[7]{81^{-3,5} } =\sqrt[7]{81^{-3\frac{1}{2} } } =\sqrt[7]{81^{-\frac{7}{2} } } =(81^{-\frac{7}{2} } )^{\frac{1}{7} } =81^{(-\frac{7}{2} )\cdot \frac{1}{7} } =81^{-\frac{1}{2} } =(9^{2} )^{-\frac{1}{2} } =9^{2\cdot (-\frac{1}{2} )} =9^{-1} =(\frac{1}{9} )^{1}=\dfrac{1}{9}[/tex]
[tex]c)\\\\(\sqrt[5]{11^{-0,8} } )^{12,5} =(\sqrt[5]{11^{-\frac{8}{10} } } )^{12\frac{1}{2} } =(\sqrt[5]{11^{-\frac{4}{5} } } )^{\frac{25}{2} } =((11^{-\frac{4}{5} } )^{\frac{1}{5} } )^{\frac{25}{2}} =11^{(-\frac{4}{5} )\cdot \frac{1}{5} \cdot \frac{25}{2} } =11^{-2} =(\frac{1}{11} )^{2} =\dfrac{1}{11} \cdot \dfrac{1}{11} =\dfrac{1}{121}[/tex]
korzystam ze wzorów:
[tex](x^{n} )^{m} =x^{n\cdot m} \\\\\sqrt[n]{x} =x^{\frac{1}{n} } \\\\\\x^{-n} =(\frac{1}{x} )^{n}[/tex]
