Solve (-3/2)^3div75/16-(-2)^4*43/8=?

$$( - \frac { 3 } { 2 } ) ^ { 3 } \div \frac { 75 } { 16 } - ( - 2 ) ^ { 4 } \times 4 \frac { 3 } { 8 } = ?$$

Evaluate

$$-\frac{1768}{25}=-70.72$$

Solution Steps

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

$$\frac{-\frac{27}{8}}{\frac{75}{16}}-\left(-2\right)^{4}\times \frac{4\times 8+3}{8}$$

Divide -\frac{27}{8} by \frac{75}{16} by multiplying -\frac{27}{8} by the reciprocal of \frac{75}{16}.

$$-\frac{27}{8}\times \frac{16}{75}-\left(-2\right)^{4}\times \frac{4\times 8+3}{8}$$

Multiply -\frac{27}{8} times \frac{16}{75} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-27\times 16}{8\times 75}-\left(-2\right)^{4}\times \frac{4\times 8+3}{8}$$

Do the multiplications in the fraction \frac{-27\times 16}{8\times 75}.

$$\frac{-432}{600}-\left(-2\right)^{4}\times \frac{4\times 8+3}{8}$$

Reduce the fraction \frac{-432}{600} to lowest terms by extracting and canceling out 24.

$$-\frac{18}{25}-\left(-2\right)^{4}\times \frac{4\times 8+3}{8}$$

Calculate -2 to the power of 4 and get 16.

$$-\frac{18}{25}-16\times \frac{4\times 8+3}{8}$$

Multiply 4 and 8 to get 32.

$$-\frac{18}{25}-16\times \frac{32+3}{8}$$

Add 32 and 3 to get 35.

$$-\frac{18}{25}-16\times \frac{35}{8}$$

Express 16\times \frac{35}{8} as a single fraction.

$$-\frac{18}{25}-\frac{16\times 35}{8}$$

Multiply 16 and 35 to get 560.

$$-\frac{18}{25}-\frac{560}{8}$$

Divide 560 by 8 to get 70.

$$-\frac{18}{25}-70$$

Convert 70 to fraction \frac{1750}{25}.

$$-\frac{18}{25}-\frac{1750}{25}$$

Since -\frac{18}{25} and \frac{1750}{25} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-18-1750}{25}$$

Subtract 1750 from -18 to get -1768.

$$-\frac{1768}{25}$$

Factor

$$-\frac{1768}{25} = -70\frac{18}{25} = -70.72$$