IDNLearner.com, seu guia para esclarecimentos rápidos e precisos. Nossos especialistas fornecem respostas rápidas e precisas para ajudá-lo a entender e resolver qualquer problema que enfrentar.

Que número real representa a expressão [tex] \frac{(0,125)^{2} + 2^{-3} }{ \frac{2}{3}^{-2} } [/tex] ?
a) 16
b) [tex] \frac{1}{16} [/tex]
c) [tex] \frac{1}{8} [/tex]
d) [tex] \frac{3}{64} [/tex]
e) [tex] \frac{64}{3} [/tex]


Sagot :

[tex]\frac{\left(0,125\right)^2+2^{-3}}{\left(\frac{2}{3}\right)^{-2}}=\\\\\\\frac{\left ( \frac{125^{\div125}}{1000^{\div125}} \right )^2+\left ( \frac{1}{2} \right )^3}{\left ( \frac{3}{2} \right )^2}=\\\\\\\frac{\left ( \frac{1}{8} \right )^2+\left ( \frac{1}{8} \right )}{\left ( \frac{9}{4} \right )}=\\\\\\\frac{\frac{1}{64}+\frac{1}{8}}{\frac{9}{4}}=\\\\\\\frac{9}{64}\div\frac{9}{4}=\\\\\\\frac{9}{64}\times \frac{4}{9}=\\\\\\\frac{4}{64}=\\\\\\\boxed{\frac{1}{16}}[/tex]

 Portanto, alternativa b.