Resolver 3^-2+5^-3/3^-2-5^-2

$$\frac { 3 ^ { - 2 } + 5 ^ { - 3 } } { 3 ^ { - 2 } - 5 ^ { - 2 } }$$

Calcular

$$\frac{67}{40}=1.675$$

Pasos da solución

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

$$\frac{\frac{1}{9}+5^{-3}}{3^{-2}-5^{-2}}$$

Calcula 5 á potencia de -3 e obtén \frac{1}{125}.

$$\frac{\frac{1}{9}+\frac{1}{125}}{3^{-2}-5^{-2}}$$

Suma \frac{1}{9} e \frac{1}{125} para obter \frac{134}{1125}.

$$\frac{\frac{134}{1125}}{3^{-2}-5^{-2}}$$

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

$$\frac{\frac{134}{1125}}{\frac{1}{9}-5^{-2}}$$

Calcula 5 á potencia de -2 e obtén \frac{1}{25}.

$$\frac{\frac{134}{1125}}{\frac{1}{9}-\frac{1}{25}}$$

Resta \frac{1}{25} de \frac{1}{9} para obter \frac{16}{225}.

$$\frac{\frac{134}{1125}}{\frac{16}{225}}$$

Divide \frac{134}{1125} entre \frac{16}{225} mediante a multiplicación de \frac{134}{1125} polo recíproco de \frac{16}{225}.

$$\frac{134}{1125}\times \frac{225}{16}$$

Multiplica \frac{134}{1125} e \frac{225}{16} para obter \frac{67}{40}.

$$\frac{67}{40}$$

Factorizar

$$\frac{67}{2 ^ {3} \cdot 5} = 1\frac{27}{40} = 1.675$$