Solve (17/76-16/93)*[0.5^{3}+(-1/2)^3]-[21/2-(-2)^2]div(-3^2+8)*(-1)^10

$$( \frac { 17 } { 76 } - \frac { 16 } { 93 } ) \times [ 0.5 ^ { 3 } + ( - \frac { 1 } { 2 } ) ^ { 3 } ] - [ 2 \frac { 1 } { 2 } - ( - 2 ) ^ { 2 } ] \div ( - 3 ^ { 2 } + 8 ) \times ( - 1 ) ^ { 10 }$$

Evaluate

$$-1.5$$

Solution Steps

Least common multiple of 76 and 93 is 7068. Convert \frac{17}{76} and \frac{16}{93} to fractions with denominator 7068.

$$\left(\frac{1581}{7068}-\frac{1216}{7068}\right)\left(0.5^{3}+\left(-\frac{1}{2}\right)^{3}\right)-\frac{\frac{2\times 2+1}{2}-\left(-2\right)^{2}}{-3^{2}+8}\left(-1\right)^{10}$$

Since \frac{1581}{7068} and \frac{1216}{7068} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1581-1216}{7068}\left(0.5^{3}+\left(-\frac{1}{2}\right)^{3}\right)-\frac{\frac{2\times 2+1}{2}-\left(-2\right)^{2}}{-3^{2}+8}\left(-1\right)^{10}$$

Subtract 1216 from 1581 to get 365.

$$\frac{365}{7068}\left(0.5^{3}+\left(-\frac{1}{2}\right)^{3}\right)-\frac{\frac{2\times 2+1}{2}-\left(-2\right)^{2}}{-3^{2}+8}\left(-1\right)^{10}$$

Calculate 0.5 to the power of 3 and get 0.125.

$$\frac{365}{7068}\left(0.125+\left(-\frac{1}{2}\right)^{3}\right)-\frac{\frac{2\times 2+1}{2}-\left(-2\right)^{2}}{-3^{2}+8}\left(-1\right)^{10}$$

Calculate -\frac{1}{2} to the power of 3 and get -\frac{1}{8}.

$$\frac{365}{7068}\left(0.125-\frac{1}{8}\right)-\frac{\frac{2\times 2+1}{2}-\left(-2\right)^{2}}{-3^{2}+8}\left(-1\right)^{10}$$

Subtract \frac{1}{8} from 0.125 to get 0.

$$\frac{365}{7068}\times 0-\frac{\frac{2\times 2+1}{2}-\left(-2\right)^{2}}{-3^{2}+8}\left(-1\right)^{10}$$

Multiply \frac{365}{7068} and 0 to get 0.

$$0-\frac{\frac{2\times 2+1}{2}-\left(-2\right)^{2}}{-3^{2}+8}\left(-1\right)^{10}$$

Multiply 2 and 2 to get 4.

$$0-\frac{\frac{4+1}{2}-\left(-2\right)^{2}}{-3^{2}+8}\left(-1\right)^{10}$$

Add 4 and 1 to get 5.

$$0-\frac{\frac{5}{2}-\left(-2\right)^{2}}{-3^{2}+8}\left(-1\right)^{10}$$

Calculate -2 to the power of 2 and get 4.

$$0-\frac{\frac{5}{2}-4}{-3^{2}+8}\left(-1\right)^{10}$$

Convert 4 to fraction \frac{8}{2}.

$$0-\frac{\frac{5}{2}-\frac{8}{2}}{-3^{2}+8}\left(-1\right)^{10}$$

Since \frac{5}{2} and \frac{8}{2} have the same denominator, subtract them by subtracting their numerators.

$$0-\frac{\frac{5-8}{2}}{-3^{2}+8}\left(-1\right)^{10}$$

Subtract 8 from 5 to get -3.

$$0-\frac{-\frac{3}{2}}{-3^{2}+8}\left(-1\right)^{10}$$

Calculate 3 to the power of 2 and get 9.

$$0-\frac{-\frac{3}{2}}{-9+8}\left(-1\right)^{10}$$

Add -9 and 8 to get -1.

$$0-\frac{-\frac{3}{2}}{-1}\left(-1\right)^{10}$$

Express \frac{-\frac{3}{2}}{-1} as a single fraction.

$$0-\frac{-3}{2\left(-1\right)}\left(-1\right)^{10}$$

Multiply 2 and -1 to get -2.

$$0-\frac{-3}{-2}\left(-1\right)^{10}$$

Fraction \frac{-3}{-2} can be simplified to \frac{3}{2} by removing the negative sign from both the numerator and the denominator.

$$0-\frac{3}{2}\left(-1\right)^{10}$$

Calculate -1 to the power of 10 and get 1.

$$0-\frac{3}{2}\times 1$$

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

$$0-\frac{3}{2}$$

Subtract \frac{3}{2} from 0 to get -\frac{3}{2}.

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

Factor

$$-1.5$$