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

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

Calcula

$$-3$$

Passos de solució

Calculeu -\frac{3}{5} elevat a 6 per obtenir \frac{729}{15625}.

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

Calculeu \frac{25}{9} elevat a 2 per obtenir \frac{625}{81}.

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

Multipliqueu \frac{729}{15625} per \frac{625}{81} per obtenir \frac{9}{25}.

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

Calculeu \frac{9}{25} elevat a 4 per obtenir \frac{6561}{390625}.

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

Calculeu \frac{9}{5} elevat a 6 per obtenir \frac{531441}{15625}.

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

Dividiu \frac{6561}{390625} per \frac{531441}{15625} multiplicant \frac{6561}{390625} pel recíproc de \frac{531441}{15625}.

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

Multipliqueu \frac{6561}{390625} per \frac{15625}{531441} per obtenir \frac{1}{2025}.

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

Calculeu 27 elevat a 2 per obtenir 729.

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

Multipliqueu \frac{1}{2025} per 729 per obtenir \frac{9}{25}.

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

Dividiu \frac{9}{25} per -\frac{3}{25} multiplicant \frac{9}{25} pel recíproc de -\frac{3}{25}.

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

Multipliqueu \frac{9}{25} per -\frac{25}{3} per obtenir -3.

$$-3$$

Factoritzar

$$-3$$