Solve (-3/2)^{3}*(-0.6)^{2}-(-4/5)^2*1.5^3-2^3div(-2/3)^3

$$( - \frac { 3 } { 2 } ) ^ { 3 } \times ( - 0.6 ) ^ { 2 } - ( - \frac { 4 } { 5 } ) ^ { 2 } \times 1.5 ^ { 3 } - 2 ^ { 3 } \div ( - \frac { 2 } { 3 } ) ^ { 3 }$$

Evaluate

$$23.625$$

Solution Steps

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

$$-\frac{27}{8}\left(-0.6\right)^{2}-\left(-\frac{4}{5}\right)^{2}\times 1.5^{3}-\frac{2^{3}}{\left(-\frac{2}{3}\right)^{3}}$$

Calculate -0.6 to the power of 2 and get 0.36.

$$-\frac{27}{8}\times 0.36-\left(-\frac{4}{5}\right)^{2}\times 1.5^{3}-\frac{2^{3}}{\left(-\frac{2}{3}\right)^{3}}$$

Convert decimal number 0.36 to fraction \frac{36}{100}. Reduce the fraction \frac{36}{100} to lowest terms by extracting and canceling out 4.

$$-\frac{27}{8}\times \frac{9}{25}-\left(-\frac{4}{5}\right)^{2}\times 1.5^{3}-\frac{2^{3}}{\left(-\frac{2}{3}\right)^{3}}$$

Multiply -\frac{27}{8} times \frac{9}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-27\times 9}{8\times 25}-\left(-\frac{4}{5}\right)^{2}\times 1.5^{3}-\frac{2^{3}}{\left(-\frac{2}{3}\right)^{3}}$$

Do the multiplications in the fraction \frac{-27\times 9}{8\times 25}.

$$\frac{-243}{200}-\left(-\frac{4}{5}\right)^{2}\times 1.5^{3}-\frac{2^{3}}{\left(-\frac{2}{3}\right)^{3}}$$

Fraction \frac{-243}{200} can be rewritten as -\frac{243}{200} by extracting the negative sign.

$$-\frac{243}{200}-\left(-\frac{4}{5}\right)^{2}\times 1.5^{3}-\frac{2^{3}}{\left(-\frac{2}{3}\right)^{3}}$$

Calculate -\frac{4}{5} to the power of 2 and get \frac{16}{25}.

$$-\frac{243}{200}-\frac{16}{25}\times 1.5^{3}-\frac{2^{3}}{\left(-\frac{2}{3}\right)^{3}}$$

Calculate 1.5 to the power of 3 and get 3.375.

$$-\frac{243}{200}-\frac{16}{25}\times 3.375-\frac{2^{3}}{\left(-\frac{2}{3}\right)^{3}}$$

Convert decimal number 3.375 to fraction \frac{3375}{1000}. Reduce the fraction \frac{3375}{1000} to lowest terms by extracting and canceling out 125.

$$-\frac{243}{200}-\frac{16}{25}\times \frac{27}{8}-\frac{2^{3}}{\left(-\frac{2}{3}\right)^{3}}$$

Multiply \frac{16}{25} times \frac{27}{8} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{243}{200}-\frac{16\times 27}{25\times 8}-\frac{2^{3}}{\left(-\frac{2}{3}\right)^{3}}$$

Do the multiplications in the fraction \frac{16\times 27}{25\times 8}.

$$-\frac{243}{200}-\frac{432}{200}-\frac{2^{3}}{\left(-\frac{2}{3}\right)^{3}}$$

Since -\frac{243}{200} and \frac{432}{200} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-243-432}{200}-\frac{2^{3}}{\left(-\frac{2}{3}\right)^{3}}$$

Subtract 432 from -243 to get -675.

$$\frac{-675}{200}-\frac{2^{3}}{\left(-\frac{2}{3}\right)^{3}}$$

Reduce the fraction \frac{-675}{200} to lowest terms by extracting and canceling out 25.

$$-\frac{27}{8}-\frac{2^{3}}{\left(-\frac{2}{3}\right)^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$-\frac{27}{8}-\frac{8}{\left(-\frac{2}{3}\right)^{3}}$$

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

$$-\frac{27}{8}-\frac{8}{-\frac{8}{27}}$$

Divide 8 by -\frac{8}{27} by multiplying 8 by the reciprocal of -\frac{8}{27}.

$$-\frac{27}{8}-8\left(-\frac{27}{8}\right)$$

Cancel out 8 and 8.

$$-\frac{27}{8}-\left(-27\right)$$

The opposite of -27 is 27.

$$-\frac{27}{8}+27$$

Convert 27 to fraction \frac{216}{8}.

$$-\frac{27}{8}+\frac{216}{8}$$

Since -\frac{27}{8} and \frac{216}{8} have the same denominator, add them by adding their numerators.

$$\frac{-27+216}{8}$$

Add -27 and 216 to get 189.

$$\frac{189}{8}$$

Factor

$$\frac{7 \cdot 3 ^ {3}}{2 ^ {3}} = 23\frac{5}{8} = 23.625$$