Question

Qual o valor da expressão

Answer 1

Vamos tentar colocar as frações com mesma base, assim temos que:

$[(\frac{1}{5^{-\frac{2}{3}}})^3-(\frac{2^{12}}{2^{10}})^{\frac{1}{2}}]-[\frac{(0,333...)^{-\frac{5}{2}}}{\sqrt{3}}-\frac{(5^{\frac{5}{3}})^2}{\sqrt[3]{5}}]=$

$[(\frac{5^0}{5^{-\frac{2}{3}}})^3-(\frac{2^{12}}{2^{10}})^{\frac{1}{2}}]-[\frac{(\frac{1}{3})^{-\frac{5}{2}}}{3^{\frac{1}{2}}}}-\frac{5^{\frac{10}{3}}}{5^{\frac{1}{3}}}]=$

$[(\frac{5^0}{5^{-\frac{2}{3}}})^3-(\frac{2^{12}}{2^{10}})^{\frac{1}{2}}]-[\frac{(3^{-1})^{-\frac{5}{2}}}{3^{\frac{1}{2}}}}-\frac{5^{\frac{10}{3}}}{5^{\frac{1}{3}}}]=$

$[(\frac{5^0}{5^{-\frac{2}{3}}})^3-(\frac{2^{12}}{2^{10}})^{\frac{1}{2}}]-[\frac{3^{\frac{5}{2}}}{3^{\frac{1}{2}}}}-\frac{5^{\frac{10}{3}}}{5^{\frac{1}{3}}}]=$

$[(5^{0+\frac{2}{3}})^3-(2^{12-10}})^{\frac{1}{2}}]-[3^{\frac{5}{2}-\frac{1}{2}}}-5^{\frac{10}{3}-\frac{1}{3}}]=$

$[(5^{\frac{2}{3}})^3-(2^2)^{\frac{1}{2}}]-[3^2-5^3]=$

$[5^2-2]-[3^2-5^3]=$

$[25-2]-[9-125]=\\\\25-2-9+125\\\\139$

Alternativa "a".