Resolver {[(-3/5)^{6}*(25/9)^2]^4:(9/5)^6*27^2}:(-3/25)

$$\{ [ ( - \frac { 3 } { 5 } ) ^ { 6 } \cdot ( \frac { 25 } { 9 } ) ^ { 2 } ] ^ { 4 } : ( \frac { 9 } { 5 } ) ^ { 6 } \cdot 27 ^ { 2 } \} : ( - \frac { 3 } { 25 } )$$

Calcular

$$-3$$

Pasos da solución

Calcula -\frac{3}{5} á potencia de 6 e obtén \frac{729}{15625}.

$$\frac{\frac{\left(\frac{729}{15625}\times \left(\frac{25}{9}\right)^{2}\right)^{4}}{\left(\frac{9}{5}\right)^{6}}\times 27^{2}}{-\frac{3}{25}}$$

Calcula \frac{25}{9} á potencia de 2 e obtén \frac{625}{81}.

$$\frac{\frac{\left(\frac{729}{15625}\times \frac{625}{81}\right)^{4}}{\left(\frac{9}{5}\right)^{6}}\times 27^{2}}{-\frac{3}{25}}$$

Multiplica \frac{729}{15625} e \frac{625}{81} para obter \frac{9}{25}.

$$\frac{\frac{\left(\frac{9}{25}\right)^{4}}{\left(\frac{9}{5}\right)^{6}}\times 27^{2}}{-\frac{3}{25}}$$

Calcula \frac{9}{25} á potencia de 4 e obtén \frac{6561}{390625}.

$$\frac{\frac{\frac{6561}{390625}}{\left(\frac{9}{5}\right)^{6}}\times 27^{2}}{-\frac{3}{25}}$$

Calcula \frac{9}{5} á potencia de 6 e obtén \frac{531441}{15625}.

$$\frac{\frac{\frac{6561}{390625}}{\frac{531441}{15625}}\times 27^{2}}{-\frac{3}{25}}$$

Divide \frac{6561}{390625} entre \frac{531441}{15625} mediante a multiplicación de \frac{6561}{390625} polo recíproco de \frac{531441}{15625}.

$$\frac{\frac{6561}{390625}\times \frac{15625}{531441}\times 27^{2}}{-\frac{3}{25}}$$

Multiplica \frac{6561}{390625} e \frac{15625}{531441} para obter \frac{1}{2025}.

$$\frac{\frac{1}{2025}\times 27^{2}}{-\frac{3}{25}}$$

Calcula 27 á potencia de 2 e obtén 729.

$$\frac{\frac{1}{2025}\times 729}{-\frac{3}{25}}$$

Multiplica \frac{1}{2025} e 729 para obter \frac{9}{25}.

$$\frac{\frac{9}{25}}{-\frac{3}{25}}$$

Divide \frac{9}{25} entre -\frac{3}{25} mediante a multiplicación de \frac{9}{25} polo recíproco de -\frac{3}{25}.

$$\frac{9}{25}\left(-\frac{25}{3}\right)$$

Multiplica \frac{9}{25} e -\frac{25}{3} para obter -3.

$$-3$$

Factorizar

$$-3$$