Solve 1-1/2left(3{left(-2/3right)}^2-1^4right)+1/4/{left(-frac{1{2}right)}^3}

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

Evaluate

$$-\frac{5}{3}\approx -1.666666667$$

Solution Steps

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

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

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

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

Multiply \frac{3}{2} times \frac{4}{9} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{3\times 4}{2\times 9}.

$$1-\frac{12}{18}\left(-1\right)^{4}+\frac{\frac{1}{4}}{\left(-\frac{1}{2}\right)^{3}}$$

Reduce the fraction \frac{12}{18} to lowest terms by extracting and canceling out 6.

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

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

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

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

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

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

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

Since \frac{3}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from 3 to get 1.

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

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

$$\frac{1}{3}+\frac{\frac{1}{4}}{-\frac{1}{8}}$$

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

$$\frac{1}{3}+\frac{1}{4}\left(-8\right)$$

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

$$\frac{1}{3}+\frac{-8}{4}$$

Divide -8 by 4 to get -2.

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

Convert 2 to fraction \frac{6}{3}.

$$\frac{1}{3}-\frac{6}{3}$$

Since \frac{1}{3} and \frac{6}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-6}{3}$$

Subtract 6 from 1 to get -5.

$$-\frac{5}{3}$$

Factor

$$-\frac{5}{3} = -1\frac{2}{3} = -1.6666666666666667$$