Question

Efetuar $[ 5^{0} * 5^{-1} + (\frac{1}{2}) ^{-1} * \frac{1}{5} ]^{-1}$

meu resultado final deu 5/23
mas o gabarito consta 5/3

Answer 1

vamos por partes:
$\displaystyle 5^{-1}=\frac{1}{5}\\\\5^{0}=1\\\\\left(\frac{1}{2}\right)^{-1}=\frac{2}{1}$
Então:
$\displaystyle\left[5^{0}\cdot 5^{-1}+\left(\frac{1}{2}\right)^{-1}\cdot\frac{1}{5}\right]^{-1}\ pode~ser~escrito~como:\\\\\left[1\cdot\frac{1}{5}+\frac{2}{1}\cdot\frac{1}{5}\right]^{-1}=\left[\frac{1}{5}+2\cdot\frac{1}{5}\right]^{-1}\ e~resolvido:\\\\ \left[\frac{1}{5}+\frac{2}{5}\right]^{-1}=\left[\frac{3}{5}\right]^{-1}=\boxed{\frac{5}{3}}$