Solve 1/2(-4^3)-(1^2/2)(-4)+3(-1/2)(-4)(1/3)-18(frac{1^3}{2})(-4)(-frac{1^2}{3})

$$\frac{ 1 }{ 2 } (- { 4 }^{ 3 } )-( \frac{ { 1 }^{ 2 } }{ 2 } )(-4)+3(- \frac{ 1 }{ 2 } )(-4)( \frac{ 1 }{ 3 } )-18( \frac{ { 1 }^{ 3 } }{ 2 } )(-4)(- \frac{ { 1 }^{ 2 } }{ 3 } )$$

Evaluate

$$-40$$

Solution Steps

Calculate 4 to the power of 3 and get 64.

$$\frac{1}{2}\left(-64\right)-\frac{1^{2}}{2}\left(-4\right)+3\left(-\frac{1}{2}\right)\left(-4\right)\times \frac{1}{3}-18\times \frac{1^{3}}{2}\left(-4\right)\left(-\frac{1^{2}}{3}\right)$$

Multiply \frac{1}{2} and -64 to get \frac{-64}{2}.

$$\frac{-64}{2}-\frac{1^{2}}{2}\left(-4\right)+3\left(-\frac{1}{2}\right)\left(-4\right)\times \frac{1}{3}-18\times \frac{1^{3}}{2}\left(-4\right)\left(-\frac{1^{2}}{3}\right)$$

Divide -64 by 2 to get -32.

$$-32-\frac{1^{2}}{2}\left(-4\right)+3\left(-\frac{1}{2}\right)\left(-4\right)\times \frac{1}{3}-18\times \frac{1^{3}}{2}\left(-4\right)\left(-\frac{1^{2}}{3}\right)$$

Calculate 1 to the power of 2 and get 1.

$$-32-\frac{1}{2}\left(-4\right)+3\left(-\frac{1}{2}\right)\left(-4\right)\times \frac{1}{3}-18\times \frac{1^{3}}{2}\left(-4\right)\left(-\frac{1^{2}}{3}\right)$$

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

$$-32-\frac{-4}{2}+3\left(-\frac{1}{2}\right)\left(-4\right)\times \frac{1}{3}-18\times \frac{1^{3}}{2}\left(-4\right)\left(-\frac{1^{2}}{3}\right)$$

Divide -4 by 2 to get -2.

$$-32-\left(-2\right)+3\left(-\frac{1}{2}\right)\left(-4\right)\times \frac{1}{3}-18\times \frac{1^{3}}{2}\left(-4\right)\left(-\frac{1^{2}}{3}\right)$$

The opposite of -2 is 2.

$$-32+2+3\left(-\frac{1}{2}\right)\left(-4\right)\times \frac{1}{3}-18\times \frac{1^{3}}{2}\left(-4\right)\left(-\frac{1^{2}}{3}\right)$$

Add -32 and 2 to get -30.

$$-30+3\left(-\frac{1}{2}\right)\left(-4\right)\times \frac{1}{3}-18\times \frac{1^{3}}{2}\left(-4\right)\left(-\frac{1^{2}}{3}\right)$$

Express 3\left(-\frac{1}{2}\right) as a single fraction.

$$-30+\frac{3\left(-1\right)}{2}\left(-4\right)\times \frac{1}{3}-18\times \frac{1^{3}}{2}\left(-4\right)\left(-\frac{1^{2}}{3}\right)$$

Multiply 3 and -1 to get -3.

$$-30+\frac{-3}{2}\left(-4\right)\times \frac{1}{3}-18\times \frac{1^{3}}{2}\left(-4\right)\left(-\frac{1^{2}}{3}\right)$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$-30-\frac{3}{2}\left(-4\right)\times \frac{1}{3}-18\times \frac{1^{3}}{2}\left(-4\right)\left(-\frac{1^{2}}{3}\right)$$

Express -\frac{3}{2}\left(-4\right) as a single fraction.

$$-30+\frac{-3\left(-4\right)}{2}\times \frac{1}{3}-18\times \frac{1^{3}}{2}\left(-4\right)\left(-\frac{1^{2}}{3}\right)$$

Multiply -3 and -4 to get 12.

$$-30+\frac{12}{2}\times \frac{1}{3}-18\times \frac{1^{3}}{2}\left(-4\right)\left(-\frac{1^{2}}{3}\right)$$

Divide 12 by 2 to get 6.

$$-30+6\times \frac{1}{3}-18\times \frac{1^{3}}{2}\left(-4\right)\left(-\frac{1^{2}}{3}\right)$$

Multiply 6 and \frac{1}{3} to get \frac{6}{3}.

$$-30+\frac{6}{3}-18\times \frac{1^{3}}{2}\left(-4\right)\left(-\frac{1^{2}}{3}\right)$$

Divide 6 by 3 to get 2.

$$-30+2-18\times \frac{1^{3}}{2}\left(-4\right)\left(-\frac{1^{2}}{3}\right)$$

Add -30 and 2 to get -28.

$$-28-18\times \frac{1^{3}}{2}\left(-4\right)\left(-\frac{1^{2}}{3}\right)$$

Calculate 1 to the power of 3 and get 1.

$$-28-18\times \frac{1}{2}\left(-4\right)\left(-\frac{1^{2}}{3}\right)$$

Multiply 18 and \frac{1}{2} to get \frac{18}{2}.

$$-28-\frac{18}{2}\left(-4\right)\left(-\frac{1^{2}}{3}\right)$$

Divide 18 by 2 to get 9.

$$-28-9\left(-4\right)\left(-\frac{1^{2}}{3}\right)$$

Multiply 9 and -4 to get -36.

$$-28-\left(-36\left(-\frac{1^{2}}{3}\right)\right)$$

Calculate 1 to the power of 2 and get 1.

$$-28-\left(-36\left(-\frac{1}{3}\right)\right)$$

Express -36\left(-\frac{1}{3}\right) as a single fraction.

$$-28-\frac{-36\left(-1\right)}{3}$$

Multiply -36 and -1 to get 36.

$$-28-\frac{36}{3}$$

Divide 36 by 3 to get 12.

$$-28-12$$

Subtract 12 from -28 to get -40.

$$-40$$

Factor

$$-40$$