Solve -3*(-2/3)^2-4*(1-2/3)-8div(2/3)^2

$$- 3 \times ( - \frac { 2 } { 3 } ) ^ { 2 } - 4 \times ( 1 - \frac { 2 } { 3 } ) - 8 \div ( \frac { 2 } { 3 } ) ^ { 2 }$$

Evaluate

$$-\frac{62}{3}\approx -20.666666667$$

Solution Steps

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

$$-3\times \frac{4}{9}-4\left(1-\frac{2}{3}\right)-\frac{8}{\left(\frac{2}{3}\right)^{2}}$$

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

$$\frac{-3\times 4}{9}-4\left(1-\frac{2}{3}\right)-\frac{8}{\left(\frac{2}{3}\right)^{2}}$$

Multiply -3 and 4 to get -12.

$$\frac{-12}{9}-4\left(1-\frac{2}{3}\right)-\frac{8}{\left(\frac{2}{3}\right)^{2}}$$

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

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

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

$$-\frac{4}{3}-4\left(\frac{3}{3}-\frac{2}{3}\right)-\frac{8}{\left(\frac{2}{3}\right)^{2}}$$

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

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

Subtract 2 from 3 to get 1.

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

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

$$-\frac{4}{3}-\frac{4}{3}-\frac{8}{\left(\frac{2}{3}\right)^{2}}$$

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

$$\frac{-4-4}{3}-\frac{8}{\left(\frac{2}{3}\right)^{2}}$$

Subtract 4 from -4 to get -8.

$$-\frac{8}{3}-\frac{8}{\left(\frac{2}{3}\right)^{2}}$$

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

$$-\frac{8}{3}-\frac{8}{\frac{4}{9}}$$

Divide 8 by \frac{4}{9} by multiplying 8 by the reciprocal of \frac{4}{9}.

$$-\frac{8}{3}-8\times \frac{9}{4}$$

Express 8\times \frac{9}{4} as a single fraction.

$$-\frac{8}{3}-\frac{8\times 9}{4}$$

Multiply 8 and 9 to get 72.

$$-\frac{8}{3}-\frac{72}{4}$$

Divide 72 by 4 to get 18.

$$-\frac{8}{3}-18$$

Convert 18 to fraction \frac{54}{3}.

$$-\frac{8}{3}-\frac{54}{3}$$

Since -\frac{8}{3} and \frac{54}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-8-54}{3}$$

Subtract 54 from -8 to get -62.

$$-\frac{62}{3}$$

Factor

$$-\frac{62}{3} = -20\frac{2}{3} = -20.666666666666668$$