Solve (-1)^2019-(1/2-7/6)^4*(15/8-5)

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

Evaluate

$$-\frac{1}{3}\approx -0.333333333$$

Solution Steps

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

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

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

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

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

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

Multiply 1 and 8 to get 8.

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

Add 8 and 5 to get 13.

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

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

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

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

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

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

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

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

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

Factor

$$-\frac{1}{3} = -0.3333333333333333$$