Solve -57/7(-1/2)^3*(-2^4)+(-3/4)^2div3

$$- \frac { 57 } { 7 } ( - \frac { 1 } { 2 } ) ^ { 3 } \times ( - 2 ^ { 4 } ) + ( - \frac { 3 } { 4 } ) ^ { 2 } \div 3$$

Evaluate

$$-\frac{1803}{112}\approx -16.098214286$$

Solution Steps

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

$$-\frac{57}{7}\left(-\frac{1}{8}\right)\left(-2^{4}\right)+\frac{\left(-\frac{3}{4}\right)^{2}}{3}$$

Multiply -\frac{57}{7} times -\frac{1}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-57\left(-1\right)}{7\times 8}\left(-2^{4}\right)+\frac{\left(-\frac{3}{4}\right)^{2}}{3}$$

Do the multiplications in the fraction \frac{-57\left(-1\right)}{7\times 8}.

$$\frac{57}{56}\left(-2^{4}\right)+\frac{\left(-\frac{3}{4}\right)^{2}}{3}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{57}{56}\left(-16\right)+\frac{\left(-\frac{3}{4}\right)^{2}}{3}$$

Express \frac{57}{56}\left(-16\right) as a single fraction.

$$\frac{57\left(-16\right)}{56}+\frac{\left(-\frac{3}{4}\right)^{2}}{3}$$

Multiply 57 and -16 to get -912.

$$\frac{-912}{56}+\frac{\left(-\frac{3}{4}\right)^{2}}{3}$$

Reduce the fraction \frac{-912}{56} to lowest terms by extracting and canceling out 8.

$$-\frac{114}{7}+\frac{\left(-\frac{3}{4}\right)^{2}}{3}$$

Calculate -\frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$-\frac{114}{7}+\frac{\frac{9}{16}}{3}$$

Express \frac{\frac{9}{16}}{3} as a single fraction.

$$-\frac{114}{7}+\frac{9}{16\times 3}$$

Multiply 16 and 3 to get 48.

$$-\frac{114}{7}+\frac{9}{48}$$

Reduce the fraction \frac{9}{48} to lowest terms by extracting and canceling out 3.

$$-\frac{114}{7}+\frac{3}{16}$$

Least common multiple of 7 and 16 is 112. Convert -\frac{114}{7} and \frac{3}{16} to fractions with denominator 112.

$$-\frac{1824}{112}+\frac{21}{112}$$

Since -\frac{1824}{112} and \frac{21}{112} have the same denominator, add them by adding their numerators.

$$\frac{-1824+21}{112}$$

Add -1824 and 21 to get -1803.

$$-\frac{1803}{112}$$

Factor

$$-\frac{1803}{112} = -16\frac{11}{112} = -16.098214285714285$$