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

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

Avaliar

$$-3$$

Passos Para a Resolução

Calcule -\frac{3}{5} elevado a 6 e obtenha \frac{729}{15625}.

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

Calcule \frac{25}{9} elevado a 2 e obtenha \frac{625}{81}.

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

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

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

Calcule \frac{9}{25} elevado a 4 e obtenha \frac{6561}{390625}.

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

Calcule \frac{9}{5} elevado a 6 e obtenha \frac{531441}{15625}.

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

Divida \frac{6561}{390625} por \frac{531441}{15625} ao multiplicar \frac{6561}{390625} pelo recíproco de \frac{531441}{15625}.

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

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

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

Calcule 27 elevado a 2 e obtenha 729.

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

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

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

Divida \frac{9}{25} por -\frac{3}{25} ao multiplicar \frac{9}{25} pelo recíproco de -\frac{3}{25}.

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

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

$$-3$$

Fatorizar

$$-3$$