Solve {[-(+2/3-2)^{4}*(-1-1/3):(-4/3)^3+2/3]*(2-frac{7}{5})}^5:[(frac{4}{9})^3:(-frac{2}{3})^3]=

$$\{ [ - ( + \frac { 2 } { 3 } - 2 ) ^ { 4 } \cdot ( - 1 - \frac { 1 } { 3 } ) : ( - \frac { 4 } { 3 } ) ^ { 3 } + \frac { 2 } { 3 } ] \cdot ( 2 - \frac { 7 } { 5 } ) \} ^ { 5 } : [ ( \frac { 4 } { 9 } ) ^ { 3 } : ( - \frac { 2 } { 3 } ) ^ { 3 } ] =$$

Evaluate

$$\frac{4}{9}\approx 0.444444444$$

Solution Steps

Subtract 2 from \frac{2}{3} to get -\frac{4}{3}.

$$\frac{\left(\left(\frac{\left(-\left(-\frac{4}{3}\right)^{4}\right)\left(-1-\frac{1}{3}\right)}{\left(-\frac{4}{3}\right)^{3}}+\frac{2}{3}\right)\left(2-\frac{7}{5}\right)\right)^{5}}{\frac{\left(\frac{4}{9}\right)^{3}}{\left(-\frac{2}{3}\right)^{3}}}$$

Calculate -\frac{4}{3} to the power of 4 and get \frac{256}{81}.

$$\frac{\left(\left(\frac{-\frac{256}{81}\left(-1-\frac{1}{3}\right)}{\left(-\frac{4}{3}\right)^{3}}+\frac{2}{3}\right)\left(2-\frac{7}{5}\right)\right)^{5}}{\frac{\left(\frac{4}{9}\right)^{3}}{\left(-\frac{2}{3}\right)^{3}}}$$

Subtract \frac{1}{3} from -1 to get -\frac{4}{3}.

$$\frac{\left(\left(\frac{-\frac{256}{81}\left(-\frac{4}{3}\right)}{\left(-\frac{4}{3}\right)^{3}}+\frac{2}{3}\right)\left(2-\frac{7}{5}\right)\right)^{5}}{\frac{\left(\frac{4}{9}\right)^{3}}{\left(-\frac{2}{3}\right)^{3}}}$$

Multiply -\frac{256}{81} and -\frac{4}{3} to get \frac{1024}{243}.

$$\frac{\left(\left(\frac{\frac{1024}{243}}{\left(-\frac{4}{3}\right)^{3}}+\frac{2}{3}\right)\left(2-\frac{7}{5}\right)\right)^{5}}{\frac{\left(\frac{4}{9}\right)^{3}}{\left(-\frac{2}{3}\right)^{3}}}$$

Calculate -\frac{4}{3} to the power of 3 and get -\frac{64}{27}.

$$\frac{\left(\left(\frac{\frac{1024}{243}}{-\frac{64}{27}}+\frac{2}{3}\right)\left(2-\frac{7}{5}\right)\right)^{5}}{\frac{\left(\frac{4}{9}\right)^{3}}{\left(-\frac{2}{3}\right)^{3}}}$$

Divide \frac{1024}{243} by -\frac{64}{27} by multiplying \frac{1024}{243} by the reciprocal of -\frac{64}{27}.

$$\frac{\left(\left(\frac{1024}{243}\left(-\frac{27}{64}\right)+\frac{2}{3}\right)\left(2-\frac{7}{5}\right)\right)^{5}}{\frac{\left(\frac{4}{9}\right)^{3}}{\left(-\frac{2}{3}\right)^{3}}}$$

Multiply \frac{1024}{243} and -\frac{27}{64} to get -\frac{16}{9}.

$$\frac{\left(\left(-\frac{16}{9}+\frac{2}{3}\right)\left(2-\frac{7}{5}\right)\right)^{5}}{\frac{\left(\frac{4}{9}\right)^{3}}{\left(-\frac{2}{3}\right)^{3}}}$$

Add -\frac{16}{9} and \frac{2}{3} to get -\frac{10}{9}.

$$\frac{\left(-\frac{10}{9}\left(2-\frac{7}{5}\right)\right)^{5}}{\frac{\left(\frac{4}{9}\right)^{3}}{\left(-\frac{2}{3}\right)^{3}}}$$

Subtract \frac{7}{5} from 2 to get \frac{3}{5}.

$$\frac{\left(-\frac{10}{9}\times \frac{3}{5}\right)^{5}}{\frac{\left(\frac{4}{9}\right)^{3}}{\left(-\frac{2}{3}\right)^{3}}}$$

Multiply -\frac{10}{9} and \frac{3}{5} to get -\frac{2}{3}.

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

Calculate -\frac{2}{3} to the power of 5 and get -\frac{32}{243}.

$$\frac{-\frac{32}{243}}{\frac{\left(\frac{4}{9}\right)^{3}}{\left(-\frac{2}{3}\right)^{3}}}$$

Calculate \frac{4}{9} to the power of 3 and get \frac{64}{729}.

$$\frac{-\frac{32}{243}}{\frac{\frac{64}{729}}{\left(-\frac{2}{3}\right)^{3}}}$$

Calculate -\frac{2}{3} to the power of 3 and get -\frac{8}{27}.

$$\frac{-\frac{32}{243}}{\frac{\frac{64}{729}}{-\frac{8}{27}}}$$

Divide \frac{64}{729} by -\frac{8}{27} by multiplying \frac{64}{729} by the reciprocal of -\frac{8}{27}.

$$\frac{-\frac{32}{243}}{\frac{64}{729}\left(-\frac{27}{8}\right)}$$

Multiply \frac{64}{729} and -\frac{27}{8} to get -\frac{8}{27}.

$$\frac{-\frac{32}{243}}{-\frac{8}{27}}$$

Divide -\frac{32}{243} by -\frac{8}{27} by multiplying -\frac{32}{243} by the reciprocal of -\frac{8}{27}.

$$-\frac{32}{243}\left(-\frac{27}{8}\right)$$

Multiply -\frac{32}{243} and -\frac{27}{8} to get \frac{4}{9}.

$$\frac{4}{9}$$

Factor

$$\frac{2 ^ {2}}{3 ^ {2}} = 0.4444444444444444$$