Solve (3/5)^9:(27/25)^9*(9/5)^9-(3/2*frac{2}{3}-frac{2}{3})^2:frac{2}{3}

$$( \frac { 3 } { 5 } ) ^ { 9 } : ( \frac { 27 } { 25 } ) ^ { 9 } \times ( \frac { 9 } { 5 } ) ^ { 9 } - ( \frac { 3 } { 2 } \times \frac { 2 } { 3 } - \frac { 2 } { 3 } ) ^ { 2 } : \frac { 2 } { 3 }$$

Evaluate

$$\frac{5}{6}\approx 0.833333333$$

Solution Steps

Calculate \frac{3}{5} to the power of 9 and get \frac{19683}{1953125}.

$$\frac{\frac{19683}{1953125}}{\left(\frac{27}{25}\right)^{9}}\times \left(\frac{9}{5}\right)^{9}-\frac{\left(\frac{3}{2}\times \frac{2}{3}-\frac{2}{3}\right)^{2}}{\frac{2}{3}}$$

Calculate \frac{27}{25} to the power of 9 and get \frac{7625597484987}{3814697265625}.

$$\frac{\frac{19683}{1953125}}{\frac{7625597484987}{3814697265625}}\times \left(\frac{9}{5}\right)^{9}-\frac{\left(\frac{3}{2}\times \frac{2}{3}-\frac{2}{3}\right)^{2}}{\frac{2}{3}}$$

Divide \frac{19683}{1953125} by \frac{7625597484987}{3814697265625} by multiplying \frac{19683}{1953125} by the reciprocal of \frac{7625597484987}{3814697265625}.

$$\frac{19683}{1953125}\times \frac{3814697265625}{7625597484987}\times \left(\frac{9}{5}\right)^{9}-\frac{\left(\frac{3}{2}\times \frac{2}{3}-\frac{2}{3}\right)^{2}}{\frac{2}{3}}$$

Multiply \frac{19683}{1953125} and \frac{3814697265625}{7625597484987} to get \frac{1953125}{387420489}.

$$\frac{1953125}{387420489}\times \left(\frac{9}{5}\right)^{9}-\frac{\left(\frac{3}{2}\times \frac{2}{3}-\frac{2}{3}\right)^{2}}{\frac{2}{3}}$$

Calculate \frac{9}{5} to the power of 9 and get \frac{387420489}{1953125}.

$$\frac{1953125}{387420489}\times \frac{387420489}{1953125}-\frac{\left(\frac{3}{2}\times \frac{2}{3}-\frac{2}{3}\right)^{2}}{\frac{2}{3}}$$

Multiply \frac{1953125}{387420489} and \frac{387420489}{1953125} to get 1.

$$1-\frac{\left(\frac{3}{2}\times \frac{2}{3}-\frac{2}{3}\right)^{2}}{\frac{2}{3}}$$

Multiply \frac{3}{2} and \frac{2}{3} to get 1.

$$1-\frac{\left(1-\frac{2}{3}\right)^{2}}{\frac{2}{3}}$$

Subtract \frac{2}{3} from 1 to get \frac{1}{3}.

$$1-\frac{\left(\frac{1}{3}\right)^{2}}{\frac{2}{3}}$$

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$1-\frac{\frac{1}{9}}{\frac{2}{3}}$$

Divide \frac{1}{9} by \frac{2}{3} by multiplying \frac{1}{9} by the reciprocal of \frac{2}{3}.

$$1-\frac{1}{9}\times \frac{3}{2}$$

Multiply \frac{1}{9} and \frac{3}{2} to get \frac{1}{6}.

$$1-\frac{1}{6}$$

Subtract \frac{1}{6} from 1 to get \frac{5}{6}.

$$\frac{5}{6}$$

Factor

$$\frac{5}{2 \cdot 3} = 0.8333333333333334$$