Question

escreva na forma de potência:
A)
$\sqrt[4]{10 ^{2} }$
B)
$\ \sqrt[4]{ 3}^{2}$
C)
$\sqrt[5]{2}$
D)
$\sqrt[10]{6}^{2}$
E)
$\frac{1}{ \sqrt{3} }$
F)
$\frac{1}{ \sqrt[3]{10}^{2} }$
ajuda pls​

Answer 1

Resposta:

Lembre-se:

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

$(\frac{x}{y} )^{z} =(\frac{y}{x} )x^{-z}$

Então:

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

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

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

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

e) $\frac{1}{\sqrt{3} } =\frac{1}{3^{\frac{1}{2} } } =(\frac{3^{\frac{1}{2} } }{1} )^{-1} =(3^{\frac{1}{2} } )^{-1} =3^{-\frac{1}{2} }$

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