Question

Help me pls ..
Tudo isso elevado a - 1/2....


Imagem em anexo

Answer 1

Resposta:

Transformando as dízimas:

0,6666.....=6÷3/9÷3=2/3 (pegue o número que repete, nesse caso é o seis e divida-o por 9, depois simplifique)

1,333...=1+0,3333=1+3/9=(9+3)/9=12÷3/9÷3=4/3

$[\sqrt{(\frac{1}{6})^{3}.(\frac{2}{3})} +\sqrt{(\frac{2}{3})^{0}-(\frac{1}{\frac{4}{3}})}]^{-\frac{1}{2} }=$

$[\sqrt{(\frac{1^{3}}{6^{3}}).(\frac{2}{3})} +\sqrt{(1-(\frac{3}{4})}]^{-\frac{1}{2} }=$

$[\sqrt{(\frac{1}{216}).(\frac{2}{3})} +\sqrt{(\frac{4-3}{4})}]^{-\frac{1}{2}}=$

$[\sqrt{(\frac{1}{324})} +\sqrt{(\frac{1}{4})}]^{-\frac{1}{2}}=$

$(\frac{1}{18}+\frac{1}{2})^{-\frac{1}{2}}=\\(\frac{1+9}{18} )^{-\frac{1}{2}}=\\(\frac{10}{18})^{-\frac{1}{2}}=\\(\frac{5}{9})^{-\frac{1}{2}}=\\(\frac{9}{5})^{\frac{1}{2}}=\\ \sqrt{\frac{9}{5}} =\\\frac{3}{\sqrt{5}}.\frac{\sqrt{5}}{\sqrt{5}}=\\\\\frac{3}{5}.\sqrt{5}$

Propriedades:

$(a^{m})^{n}=a^{m.n}\\\\\sqrt[n]{x^m} =x^{\frac{m}{n} }\\\\a^{m}a^{n}=a^{m+n}\\\\\frac{a^{m}}{a^{n}}=a^{m-n} \\\\a^{0}=1\\\\a^{1}=a$