Solve -(1/3+frac{7/9)^{2}}{(1-1/2)^2*(-2)^3-3/2}+-(-frac{1}{6})^2+frac{frac{1}{4}-frac{1}{5}}{(1-frac{2}{5})^2}]-frac{frac{1}{3}-frac{2}{9}}{frac{1}{8}-frac{15}{8}}=

$$- \frac { ( \frac { 1 } { 3 } + \frac { 7 } { 9 } ) ^ { 2 } } { ( 1 - \frac { 1 } { 2 } ) ^ { 2 } \cdot ( - 2 ) ^ { 3 } - \frac { 3 } { 2 } } + - ( - \frac { 1 } { 6 } ) ^ { 2 } + \frac { \frac { 1 } { 4 } - \frac { 1 } { 5 } } { ( 1 - \frac { 2 } { 5 } ) ^ { 2 } } ] - \frac { \frac { 1 } { 3 } - \frac { 2 } { 9 } } { \frac { 1 } { 8 } - \frac { 15 } { 8 } } =$$

Evaluate

$$\frac{263}{567}\approx 0.463844797$$

Solution Steps

Add \frac{1}{3} and \frac{7}{9} to get \frac{10}{9}.

$$-\frac{\left(\frac{10}{9}\right)^{2}}{\left(1-\frac{1}{2}\right)^{2}\left(-2\right)^{3}-\frac{3}{2}}-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}$$

Calculate \frac{10}{9} to the power of 2 and get \frac{100}{81}.

$$-\frac{\frac{100}{81}}{\left(1-\frac{1}{2}\right)^{2}\left(-2\right)^{3}-\frac{3}{2}}-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}$$

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

$$-\frac{\frac{100}{81}}{\left(\frac{1}{2}\right)^{2}\left(-2\right)^{3}-\frac{3}{2}}-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$-\frac{\frac{100}{81}}{\frac{1}{4}\left(-2\right)^{3}-\frac{3}{2}}-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}$$

Calculate -2 to the power of 3 and get -8.

$$-\frac{\frac{100}{81}}{\frac{1}{4}\left(-8\right)-\frac{3}{2}}-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}$$

Multiply \frac{1}{4} and -8 to get -2.

$$-\frac{\frac{100}{81}}{-2-\frac{3}{2}}-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}$$

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

$$-\frac{\frac{100}{81}}{-\frac{7}{2}}-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}$$

Divide \frac{100}{81} by -\frac{7}{2} by multiplying \frac{100}{81} by the reciprocal of -\frac{7}{2}.

$$-\frac{100}{81}\left(-\frac{2}{7}\right)-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}$$

Multiply \frac{100}{81} and -\frac{2}{7} to get -\frac{200}{567}.

$$-\left(-\frac{200}{567}\right)-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}$$

The opposite of -\frac{200}{567} is \frac{200}{567}.

$$\frac{200}{567}-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}$$

Calculate -\frac{1}{6} to the power of 2 and get \frac{1}{36}.

$$\frac{200}{567}-\frac{1}{36}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}$$

Subtract \frac{1}{36} from \frac{200}{567} to get \frac{737}{2268}.

$$\frac{737}{2268}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}$$

Subtract \frac{1}{5} from \frac{1}{4} to get \frac{1}{20}.

$$\frac{737}{2268}+\frac{\frac{1}{20}}{\left(1-\frac{2}{5}\right)^{2}}$$

Subtract \frac{2}{5} from 1 to get \frac{3}{5}.

$$\frac{737}{2268}+\frac{\frac{1}{20}}{\left(\frac{3}{5}\right)^{2}}$$

Calculate \frac{3}{5} to the power of 2 and get \frac{9}{25}.

$$\frac{737}{2268}+\frac{\frac{1}{20}}{\frac{9}{25}}$$

Divide \frac{1}{20} by \frac{9}{25} by multiplying \frac{1}{20} by the reciprocal of \frac{9}{25}.

$$\frac{737}{2268}+\frac{1}{20}\times \frac{25}{9}$$

Multiply \frac{1}{20} and \frac{25}{9} to get \frac{5}{36}.

$$\frac{737}{2268}+\frac{5}{36}$$

Add \frac{737}{2268} and \frac{5}{36} to get \frac{263}{567}.

$$\frac{263}{567}$$

Factor

$$\frac{263}{3 ^ {4} \cdot 7} = 0.4638447971781305$$