Solve [-4^2-(-1)^3*(-2)^3]div22/3*(-1/2)^2

$$[ - 4 ^ { 2 } - ( - 1 ) ^ { 3 } \times ( - 2 ) ^ { 3 } ] \div 2 \frac { 2 } { 3 } \times ( - \frac { 1 } { 2 } ) ^ { 2 }$$

Evaluate

$$-\frac{9}{4}=-2.25$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

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

Calculate -1 to the power of 3 and get -1.

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

Calculate -2 to the power of 3 and get -8.

$$\frac{-16-\left(-\left(-8\right)\right)}{\frac{2\times 3+2}{3}}\left(-\frac{1}{2}\right)^{2}$$

Multiply -1 and -8 to get 8.

$$\frac{-16-8}{\frac{2\times 3+2}{3}}\left(-\frac{1}{2}\right)^{2}$$

Subtract 8 from -16 to get -24.

$$\frac{-24}{\frac{2\times 3+2}{3}}\left(-\frac{1}{2}\right)^{2}$$

Multiply 2 and 3 to get 6.

$$\frac{-24}{\frac{6+2}{3}}\left(-\frac{1}{2}\right)^{2}$$

Add 6 and 2 to get 8.

$$\frac{-24}{\frac{8}{3}}\left(-\frac{1}{2}\right)^{2}$$

Divide -24 by \frac{8}{3} by multiplying -24 by the reciprocal of \frac{8}{3}.

$$-24\times \frac{3}{8}\left(-\frac{1}{2}\right)^{2}$$

Express -24\times \frac{3}{8} as a single fraction.

$$\frac{-24\times 3}{8}\left(-\frac{1}{2}\right)^{2}$$

Multiply -24 and 3 to get -72.

$$\frac{-72}{8}\left(-\frac{1}{2}\right)^{2}$$

Divide -72 by 8 to get -9.

$$-9\left(-\frac{1}{2}\right)^{2}$$

Calculate -\frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$-9\times \frac{1}{4}$$

Multiply -9 and \frac{1}{4} to get \frac{-9}{4}.

$$\frac{-9}{4}$$

Fraction \frac{-9}{4} can be rewritten as -\frac{9}{4} by extracting the negative sign.

$$-\frac{9}{4}$$

Factor

$$-\frac{9}{4} = -2\frac{1}{4} = -2.25$$