Resposta:

Lembre-se:

[tex]\sqrt[x]{a^{y} } =a^{\frac{y}{x} }[/tex]

[tex](\frac{x}{y} )^{z} =(\frac{y}{x} )x^{-z}[/tex]

Então:

a) [tex]\sqrt[4]{10^{2} } =10^{\frac{2}{4} } =10^{\frac{1}{2} }[/tex]

b) [tex]\sqrt[4]{3} ^{2} =(3^{\frac{1}{4} })^{2} =3^{\frac{2}{4} } =3^{\frac{1}{2} }[/tex]

c) [tex]\sqrt[5]{2} =2^{\frac{1}{5} }[/tex]

d) [tex]\sqrt[10]{6}^{2} =(6^{\frac{1}{10} } )^{2} =6^{\frac{2}{10} }=6^{\frac{1}{5} }[/tex]

e) [tex]\frac{1}{\sqrt{3} } =\frac{1}{3^{\frac{1}{2} } } =(\frac{3^{\frac{1}{2} } }{1} )^{-1} =(3^{\frac{1}{2} } )^{-1} =3^{-\frac{1}{2} }[/tex]

f) [tex]\frac{1}{\sqrt[3]{10}^{2} } =\frac{1}{(10^{\frac{1}{3} } )^{2} } =\frac{1}{10^{\frac{2}{3} } } =10^{-\frac{2}{3} }[/tex]