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

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

Evaluate

$$-3$$

Solution Steps

Calculate -\frac{3}{5} to the power of 6 and get \frac{729}{15625}.

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

Calculate \frac{25}{9} to the power of 2 and get \frac{625}{81}.

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

Multiply \frac{729}{15625} and \frac{625}{81} to get \frac{9}{25}.

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

Calculate \frac{9}{25} to the power of 4 and get \frac{6561}{390625}.

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

Calculate \frac{9}{5} to the power of 6 and get \frac{531441}{15625}.

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

Divide \frac{6561}{390625} by \frac{531441}{15625} by multiplying \frac{6561}{390625} by the reciprocal of \frac{531441}{15625}.

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

Multiply \frac{6561}{390625} and \frac{15625}{531441} to get \frac{1}{2025}.

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

Calculate 27 to the power of 2 and get 729.

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

Multiply \frac{1}{2025} and 729 to get \frac{9}{25}.

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

Divide \frac{9}{25} by -\frac{3}{25} by multiplying \frac{9}{25} by the reciprocal of -\frac{3}{25}.

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

Multiply \frac{9}{25} and -\frac{25}{3} to get -3.

$$-3$$

Factor

$$-3$$