Resolver [(5/3)^4+(3/5)^-2]div17/9

$$[ ( \frac { 5 } { 3 } ) ^ { 4 } + ( \frac { 3 } { 5 } ) ^ { - 2 } ] \div \frac { 17 } { 9 }$$

Calcular

$$\frac{50}{9}\approx 5.555555556$$

Pasos da solución

Calcula \frac{5}{3} á potencia de 4 e obtén \frac{625}{81}.

$$\frac{\frac{625}{81}+\left(\frac{3}{5}\right)^{-2}}{\frac{17}{9}}$$

Calcula \frac{3}{5} á potencia de -2 e obtén \frac{25}{9}.

$$\frac{\frac{625}{81}+\frac{25}{9}}{\frac{17}{9}}$$

Suma \frac{625}{81} e \frac{25}{9} para obter \frac{850}{81}.

$$\frac{\frac{850}{81}}{\frac{17}{9}}$$

Divide \frac{850}{81} entre \frac{17}{9} mediante a multiplicación de \frac{850}{81} polo recíproco de \frac{17}{9}.

$$\frac{850}{81}\times \frac{9}{17}$$

Multiplica \frac{850}{81} e \frac{9}{17} para obter \frac{50}{9}.

$$\frac{50}{9}$$

Factorizar

$$\frac{2 \cdot 5 ^ {2}}{3 ^ {2}} = 5\frac{5}{9} = 5.555555555555555$$