Solve 1-1/2*[3*(-2/3)^2-(-1)^4]+1/4div(-1/2)^3

$$1 - \frac { 1 } { 2 } \times [ 3 \times ( - \frac { 2 } { 3 } ) ^ { 2 } - ( - 1 ) ^ { 4 } ] + \frac { 1 } { 4 } \div ( - \frac { 1 } { 2 } ) ^ { 3 }$$

Evaluate

$$-\frac{7}{6}\approx -1.166666667$$

Solution Steps

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

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

Express 3\times \frac{4}{9} as a single fraction.

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

Multiply 3 and 4 to get 12.

$$1-\frac{1}{2}\left(\frac{12}{9}-\left(-1\right)^{4}\right)+\frac{\frac{1}{4}}{\left(-\frac{1}{2}\right)^{3}}$$

Reduce the fraction \frac{12}{9} to lowest terms by extracting and canceling out 3.

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

Calculate -1 to the power of 4 and get 1.

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

Convert 1 to fraction \frac{3}{3}.

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

Since \frac{4}{3} and \frac{3}{3} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 3 from 4 to get 1.

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

Multiply \frac{1}{2} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\times 1}{2\times 3}.

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

Convert 1 to fraction \frac{6}{6}.

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

Since \frac{6}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 6 to get 5.

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

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

$$\frac{5}{6}+\frac{\frac{1}{4}}{-\frac{1}{8}}$$

Divide \frac{1}{4} by -\frac{1}{8} by multiplying \frac{1}{4} by the reciprocal of -\frac{1}{8}.

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

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

$$\frac{5}{6}+\frac{-8}{4}$$

Divide -8 by 4 to get -2.

$$\frac{5}{6}-2$$

Convert 2 to fraction \frac{12}{6}.

$$\frac{5}{6}-\frac{12}{6}$$

Since \frac{5}{6} and \frac{12}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-12}{6}$$

Subtract 12 from 5 to get -7.

$$-\frac{7}{6}$$

Factor

$$-\frac{7}{6} = -1\frac{1}{6} = -1.1666666666666667$$