Resolver (2)^{-1}+[2/3-2^-1*((2/3)^-2*2/3+5^0)]^-1=

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

Calcular

$$-\frac{17}{14}\approx -1.214285714$$

Pasos da solución

Para multiplicar potencias da mesma base, suma os seus expoñentes. Suma -2 e 1 para obter -1.

$$2^{-1}+\left(\frac{2}{3}-2^{-1}\left(\left(\frac{2}{3}\right)^{-1}+5^{0}\right)\right)^{-1}$$

Calcula 2 á potencia de -1 e obtén \frac{1}{2}.

$$\frac{1}{2}+\left(\frac{2}{3}-2^{-1}\left(\left(\frac{2}{3}\right)^{-1}+5^{0}\right)\right)^{-1}$$

Calcula 2 á potencia de -1 e obtén \frac{1}{2}.

$$\frac{1}{2}+\left(\frac{2}{3}-\frac{1}{2}\left(\left(\frac{2}{3}\right)^{-1}+5^{0}\right)\right)^{-1}$$

Calcula \frac{2}{3} á potencia de -1 e obtén \frac{3}{2}.

$$\frac{1}{2}+\left(\frac{2}{3}-\frac{1}{2}\left(\frac{3}{2}+5^{0}\right)\right)^{-1}$$

Calcula 5 á potencia de 0 e obtén 1.

$$\frac{1}{2}+\left(\frac{2}{3}-\frac{1}{2}\left(\frac{3}{2}+1\right)\right)^{-1}$$

Suma \frac{3}{2} e 1 para obter \frac{5}{2}.

$$\frac{1}{2}+\left(\frac{2}{3}-\frac{1}{2}\times \frac{5}{2}\right)^{-1}$$

Multiplica \frac{1}{2} e \frac{5}{2} para obter \frac{5}{4}.

$$\frac{1}{2}+\left(\frac{2}{3}-\frac{5}{4}\right)^{-1}$$

Resta \frac{5}{4} de \frac{2}{3} para obter -\frac{7}{12}.

$$\frac{1}{2}+\left(-\frac{7}{12}\right)^{-1}$$

Calcula -\frac{7}{12} á potencia de -1 e obtén -\frac{12}{7}.

$$\frac{1}{2}-\frac{12}{7}$$

Resta \frac{12}{7} de \frac{1}{2} para obter -\frac{17}{14}.

$$-\frac{17}{14}$$

Factorizar

$$-\frac{17}{14} = -1\frac{3}{14} = -1.2142857142857142$$