Solve 2019+4/5*[(-4/3)^2+(-2/3)^2div(-0.16)]div(-2frac{2/5)}{(-1)^2019-(frac{1}{2}-frac{7}{6})^4*(1frac{5}{8}-5)}

$$\frac { 2019 + \frac { 4 } { 5 } \times [ ( - \frac { 4 } { 3 } ) ^ { 2 } + ( - \frac { 2 } { 3 } ) ^ { 2 } \div ( - 0.16 ) ] \div ( - 2 \frac { 2 } { 5 } ) } { ( - 1 ) ^ { 2019 } - ( \frac { 1 } { 2 } - \frac { 7 } { 6 } ) ^ { 4 } \times ( 1 \frac { 5 } { 8 } - 5 ) }$$

Evaluate

$$-6058$$

Solution Steps

Calculate -\frac{4}{3} to the power of 2 and get \frac{16}{9}.

$$\frac{2019+\frac{\frac{4}{5}\left(\frac{16}{9}+\frac{\left(-\frac{2}{3}\right)^{2}}{-0.16}\right)}{-\frac{2\times 5+2}{5}}}{\left(-1\right)^{2019}-\left(\frac{1}{2}-\frac{7}{6}\right)^{4}\left(\frac{1\times 8+5}{8}-5\right)}$$

Calculate -\frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$\frac{2019+\frac{\frac{4}{5}\left(\frac{16}{9}+\frac{\frac{4}{9}}{-0.16}\right)}{-\frac{2\times 5+2}{5}}}{\left(-1\right)^{2019}-\left(\frac{1}{2}-\frac{7}{6}\right)^{4}\left(\frac{1\times 8+5}{8}-5\right)}$$

Express \frac{\frac{4}{9}}{-0.16} as a single fraction.

$$\frac{2019+\frac{\frac{4}{5}\left(\frac{16}{9}+\frac{4}{9\left(-0.16\right)}\right)}{-\frac{2\times 5+2}{5}}}{\left(-1\right)^{2019}-\left(\frac{1}{2}-\frac{7}{6}\right)^{4}\left(\frac{1\times 8+5}{8}-5\right)}$$

Multiply 9 and -0.16 to get -1.44.

$$\frac{2019+\frac{\frac{4}{5}\left(\frac{16}{9}+\frac{4}{-1.44}\right)}{-\frac{2\times 5+2}{5}}}{\left(-1\right)^{2019}-\left(\frac{1}{2}-\frac{7}{6}\right)^{4}\left(\frac{1\times 8+5}{8}-5\right)}$$

Expand \frac{4}{-1.44} by multiplying both numerator and the denominator by 100.

$$\frac{2019+\frac{\frac{4}{5}\left(\frac{16}{9}+\frac{400}{-144}\right)}{-\frac{2\times 5+2}{5}}}{\left(-1\right)^{2019}-\left(\frac{1}{2}-\frac{7}{6}\right)^{4}\left(\frac{1\times 8+5}{8}-5\right)}$$

Reduce the fraction \frac{400}{-144} to lowest terms by extracting and canceling out 16.

$$\frac{2019+\frac{\frac{4}{5}\left(\frac{16}{9}-\frac{25}{9}\right)}{-\frac{2\times 5+2}{5}}}{\left(-1\right)^{2019}-\left(\frac{1}{2}-\frac{7}{6}\right)^{4}\left(\frac{1\times 8+5}{8}-5\right)}$$

Subtract \frac{25}{9} from \frac{16}{9} to get -1.

$$\frac{2019+\frac{\frac{4}{5}\left(-1\right)}{-\frac{2\times 5+2}{5}}}{\left(-1\right)^{2019}-\left(\frac{1}{2}-\frac{7}{6}\right)^{4}\left(\frac{1\times 8+5}{8}-5\right)}$$

Multiply \frac{4}{5} and -1 to get -\frac{4}{5}.

$$\frac{2019+\frac{-\frac{4}{5}}{-\frac{2\times 5+2}{5}}}{\left(-1\right)^{2019}-\left(\frac{1}{2}-\frac{7}{6}\right)^{4}\left(\frac{1\times 8+5}{8}-5\right)}$$

Multiply 2 and 5 to get 10.

$$\frac{2019+\frac{-\frac{4}{5}}{-\frac{10+2}{5}}}{\left(-1\right)^{2019}-\left(\frac{1}{2}-\frac{7}{6}\right)^{4}\left(\frac{1\times 8+5}{8}-5\right)}$$

Add 10 and 2 to get 12.

$$\frac{2019+\frac{-\frac{4}{5}}{-\frac{12}{5}}}{\left(-1\right)^{2019}-\left(\frac{1}{2}-\frac{7}{6}\right)^{4}\left(\frac{1\times 8+5}{8}-5\right)}$$

Divide -\frac{4}{5} by -\frac{12}{5} by multiplying -\frac{4}{5} by the reciprocal of -\frac{12}{5}.

$$\frac{2019-\frac{4}{5}\left(-\frac{5}{12}\right)}{\left(-1\right)^{2019}-\left(\frac{1}{2}-\frac{7}{6}\right)^{4}\left(\frac{1\times 8+5}{8}-5\right)}$$

Multiply -\frac{4}{5} and -\frac{5}{12} to get \frac{1}{3}.

$$\frac{2019+\frac{1}{3}}{\left(-1\right)^{2019}-\left(\frac{1}{2}-\frac{7}{6}\right)^{4}\left(\frac{1\times 8+5}{8}-5\right)}$$

Add 2019 and \frac{1}{3} to get \frac{6058}{3}.

$$\frac{\frac{6058}{3}}{\left(-1\right)^{2019}-\left(\frac{1}{2}-\frac{7}{6}\right)^{4}\left(\frac{1\times 8+5}{8}-5\right)}$$

Calculate -1 to the power of 2019 and get -1.

$$\frac{\frac{6058}{3}}{-1-\left(\frac{1}{2}-\frac{7}{6}\right)^{4}\left(\frac{1\times 8+5}{8}-5\right)}$$

Subtract \frac{7}{6} from \frac{1}{2} to get -\frac{2}{3}.

$$\frac{\frac{6058}{3}}{-1-\left(-\frac{2}{3}\right)^{4}\left(\frac{1\times 8+5}{8}-5\right)}$$

Calculate -\frac{2}{3} to the power of 4 and get \frac{16}{81}.

$$\frac{\frac{6058}{3}}{-1-\frac{16}{81}\left(\frac{1\times 8+5}{8}-5\right)}$$

Multiply 1 and 8 to get 8.

$$\frac{\frac{6058}{3}}{-1-\frac{16}{81}\left(\frac{8+5}{8}-5\right)}$$

Add 8 and 5 to get 13.

$$\frac{\frac{6058}{3}}{-1-\frac{16}{81}\left(\frac{13}{8}-5\right)}$$

Subtract 5 from \frac{13}{8} to get -\frac{27}{8}.

$$\frac{\frac{6058}{3}}{-1-\frac{16}{81}\left(-\frac{27}{8}\right)}$$

Multiply \frac{16}{81} and -\frac{27}{8} to get -\frac{2}{3}.

$$\frac{\frac{6058}{3}}{-1-\left(-\frac{2}{3}\right)}$$

The opposite of -\frac{2}{3} is \frac{2}{3}.

$$\frac{\frac{6058}{3}}{-1+\frac{2}{3}}$$

Add -1 and \frac{2}{3} to get -\frac{1}{3}.

$$\frac{\frac{6058}{3}}{-\frac{1}{3}}$$

Divide \frac{6058}{3} by -\frac{1}{3} by multiplying \frac{6058}{3} by the reciprocal of -\frac{1}{3}.

$$\frac{6058}{3}\left(-3\right)$$

Multiply \frac{6058}{3} and -3 to get -6058.

$$-6058$$

Factor

$$-6058$$