Solve (-3-1)*(-frac{3}2^3)^2-2^-1div(-1/2)^3

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

Evaluate

$$-\frac{665}{16}=-41.5625$$

Solution Steps

Subtract 1 from -3 to get -4.

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

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

$$-4\left(-\frac{27}{8}\right)^{2}-\frac{2^{-1}}{\left(-\frac{1}{2}\right)^{3}}$$

Calculate -\frac{27}{8} to the power of 2 and get \frac{729}{64}.

$$-4\times \frac{729}{64}-\frac{2^{-1}}{\left(-\frac{1}{2}\right)^{3}}$$

Multiply -4 and \frac{729}{64} to get -\frac{729}{16}.

$$-\frac{729}{16}-\frac{2^{-1}}{\left(-\frac{1}{2}\right)^{3}}$$

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

$$-\frac{729}{16}-\frac{\frac{1}{2}}{\left(-\frac{1}{2}\right)^{3}}$$

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

$$-\frac{729}{16}-\frac{\frac{1}{2}}{-\frac{1}{8}}$$

Divide \frac{1}{2} by -\frac{1}{8} by multiplying \frac{1}{2} by the reciprocal of -\frac{1}{8}.

$$-\frac{729}{16}-\frac{1}{2}\left(-8\right)$$

Multiply \frac{1}{2} and -8 to get -4.

$$-\frac{729}{16}-\left(-4\right)$$

The opposite of -4 is 4.

$$-\frac{729}{16}+4$$

Add -\frac{729}{16} and 4 to get -\frac{665}{16}.

$$-\frac{665}{16}$$

Factor

$$-\frac{665}{16} = -41\frac{9}{16} = -41.5625$$