Odpowiedź:
zad2.5
a)[tex]\sqrt[20]{3} *\sqrt[12]{27} =3^{\frac{1}{20}} *(3^3)^{\frac{1}{12} }=3^{\frac{1}{20}} *3^{\frac{1}{4} }=3^{\frac{1}{20} }*3^{\frac{5}{20}} =3^{\frac{1}{20} +\frac{5}{20} }}=3^\frac{6}{20} }=3^{\frac{3}{10} }[/tex]
b)[tex]\frac{3^{\frac{1}{2}}*\sqrt[3]{9} *3^{-\frac{1}{2} } }{81^{\frac{1}{2} }*27^{\frac{2}{3}} } =\frac{3^{\frac{1}{2}-\frac{1}{2}}*(3^2)^{\frac{1}{3} } }{(3^4)^{\frac{1}{2}}*(3^3)^{\frac{1}{3}} } =\frac{3^{\frac{2}{3} }}{3^2*3^2} =3^{\frac{2}{3} -4}}=3^{-\frac{10}{3} }=(\frac{1}{3} )^{\frac{10}{3} }[/tex]
d)[tex]\frac{2^{\frac{5}{4}}+3*2^{\frac{1}{4} }-2*3^{\frac{1}{4} } -3^{\frac{5}{4} }}{2^{\frac{1}{2}}-3^{\frac{1}{2} } } *(2^{\frac{1}{4} }+3^{\frac{1}{4} })=\frac{2^{\frac{1}{4}}(2^{\frac{4}{4} }+3)-3^{\frac{1}{4}}(2+3^{\frac{4}{4} } )}{2^{\frac{1}{2}}-3^{\frac{1}{3}} } *(2^{\frac{1}{4}}+3^{\frac{1}{4} })=\frac{5*2^{\frac{1}{4}}-5*3^{\frac{1}{4}} }{2^{\frac{1}{2}}-3^{\frac{1}{2} } } (2^{\frac{1}{4} }+3^{\frac{1}{4} })=5[/tex]
Szczegółowe wyjaśnienie:
