Solve {1/3-1/2*(-2/3)^3*9}-(-2/5)^2div(-0.8)

$$\{ \frac { 1 } { 3 } - \frac { 1 } { 2 } \times ( - \frac { 2 } { 3 } ) ^ { 3 } \times 9 \} - ( - \frac { 2 } { 5 } ) ^ { 2 } \div ( - 0.8 )$$

Evaluate

$$\frac{28}{15}\approx 1.866666667$$

Solution Steps

Calculate -\frac{2}{3} to the power of 3 and get -\frac{8}{27}.

$$\frac{1}{3}-\frac{1}{2}\left(-\frac{8}{27}\right)\times 9-\frac{\left(-\frac{2}{5}\right)^{2}}{-0.8}$$

Multiply \frac{1}{2} times -\frac{8}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{3}-\frac{1\left(-8\right)}{2\times 27}\times 9-\frac{\left(-\frac{2}{5}\right)^{2}}{-0.8}$$

Do the multiplications in the fraction \frac{1\left(-8\right)}{2\times 27}.

$$\frac{1}{3}-\frac{-8}{54}\times 9-\frac{\left(-\frac{2}{5}\right)^{2}}{-0.8}$$

Reduce the fraction \frac{-8}{54} to lowest terms by extracting and canceling out 2.

$$\frac{1}{3}-\left(-\frac{4}{27}\times 9\right)-\frac{\left(-\frac{2}{5}\right)^{2}}{-0.8}$$

Express -\frac{4}{27}\times 9 as a single fraction.

$$\frac{1}{3}-\frac{-4\times 9}{27}-\frac{\left(-\frac{2}{5}\right)^{2}}{-0.8}$$

Multiply -4 and 9 to get -36.

$$\frac{1}{3}-\frac{-36}{27}-\frac{\left(-\frac{2}{5}\right)^{2}}{-0.8}$$

Reduce the fraction \frac{-36}{27} to lowest terms by extracting and canceling out 9.

$$\frac{1}{3}-\left(-\frac{4}{3}\right)-\frac{\left(-\frac{2}{5}\right)^{2}}{-0.8}$$

The opposite of -\frac{4}{3} is \frac{4}{3}.

$$\frac{1}{3}+\frac{4}{3}-\frac{\left(-\frac{2}{5}\right)^{2}}{-0.8}$$

Since \frac{1}{3} and \frac{4}{3} have the same denominator, add them by adding their numerators.

$$\frac{1+4}{3}-\frac{\left(-\frac{2}{5}\right)^{2}}{-0.8}$$

Add 1 and 4 to get 5.

$$\frac{5}{3}-\frac{\left(-\frac{2}{5}\right)^{2}}{-0.8}$$

Calculate -\frac{2}{5} to the power of 2 and get \frac{4}{25}.

$$\frac{5}{3}-\frac{\frac{4}{25}}{-0.8}$$

Express \frac{\frac{4}{25}}{-0.8} as a single fraction.

$$\frac{5}{3}-\frac{4}{25\left(-0.8\right)}$$

Multiply 25 and -0.8 to get -20.

$$\frac{5}{3}-\frac{4}{-20}$$

Reduce the fraction \frac{4}{-20} to lowest terms by extracting and canceling out 4.

$$\frac{5}{3}-\left(-\frac{1}{5}\right)$$

The opposite of -\frac{1}{5} is \frac{1}{5}.

$$\frac{5}{3}+\frac{1}{5}$$

Least common multiple of 3 and 5 is 15. Convert \frac{5}{3} and \frac{1}{5} to fractions with denominator 15.

$$\frac{25}{15}+\frac{3}{15}$$

Since \frac{25}{15} and \frac{3}{15} have the same denominator, add them by adding their numerators.

$$\frac{25+3}{15}$$

Add 25 and 3 to get 28.

$$\frac{28}{15}$$

Factor

$$\frac{7 \cdot 2 ^ {2}}{3 \cdot 5} = 1\frac{13}{15} = 1.8666666666666667$$