Resolver (1/3)^-2+(2/3)^-2+(1/4)^-2

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

Calcular

$$\frac{109}{4}=27.25$$

Pasos da solución

Calcula \frac{1}{3} á potencia de -2 e obtén 9.

$$9+\left(\frac{2}{3}\right)^{-2}+\left(\frac{1}{4}\right)^{-2}$$

Calcula \frac{2}{3} á potencia de -2 e obtén \frac{9}{4}.

$$9+\frac{9}{4}+\left(\frac{1}{4}\right)^{-2}$$

Suma 9 e \frac{9}{4} para obter \frac{45}{4}.

$$\frac{45}{4}+\left(\frac{1}{4}\right)^{-2}$$

Calcula \frac{1}{4} á potencia de -2 e obtén 16.

$$\frac{45}{4}+16$$

Suma \frac{45}{4} e 16 para obter \frac{109}{4}.

$$\frac{109}{4}$$

Factorizar

$$\frac{109}{2 ^ {2}} = 27\frac{1}{4} = 27.25$$