Solve [(-1)^{3}div2/9+2^{200}*(-05)^200-3^3*(-3/2)^2]div|-4div2*(-1/2)^2|

$$[ ( - 1 ) ^ { 3 } \div \frac { 2 } { 9 } + 2 ^ { 200 } \times ( - 05 ) ^ { 200 } - 3 ^ { 3 } \times ( - \frac { 3 } { 2 } ) ^ { 2 } ] \div | - 4 \div 2 \times ( - \frac { 1 } { 2 } ) ^ { 2 } |$$

Evaluate

$$-\frac{261}{2}=-130.5$$

Solution Steps

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

$$\frac{\frac{-1}{\frac{2}{9}}+2^{200}\times \left(0\times 5\right)^{200}-3^{3}\left(-\frac{3}{2}\right)^{2}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

Divide -1 by \frac{2}{9} by multiplying -1 by the reciprocal of \frac{2}{9}.

$$\frac{-\frac{9}{2}+2^{200}\times \left(0\times 5\right)^{200}-3^{3}\left(-\frac{3}{2}\right)^{2}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

Calculate 2 to the power of 200 and get 1606938044258990275541962092341162602522202993782792835301376.

$$\frac{-\frac{9}{2}+1606938044258990275541962092341162602522202993782792835301376\times \left(0\times 5\right)^{200}-3^{3}\left(-\frac{3}{2}\right)^{2}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

Multiply 0 and 5 to get 0.

$$\frac{-\frac{9}{2}+1606938044258990275541962092341162602522202993782792835301376\times 0^{200}-3^{3}\left(-\frac{3}{2}\right)^{2}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

Calculate 0 to the power of 200 and get 0.

$$\frac{-\frac{9}{2}+1606938044258990275541962092341162602522202993782792835301376\times 0-3^{3}\left(-\frac{3}{2}\right)^{2}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

Multiply 1606938044258990275541962092341162602522202993782792835301376 and 0 to get 0.

$$\frac{-\frac{9}{2}+0-3^{3}\left(-\frac{3}{2}\right)^{2}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

Add -\frac{9}{2} and 0 to get -\frac{9}{2}.

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

Calculate 3 to the power of 3 and get 27.

$$\frac{-\frac{9}{2}-27\left(-\frac{3}{2}\right)^{2}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

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

$$\frac{-\frac{9}{2}-27\times \frac{9}{4}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

Multiply 27 and \frac{9}{4} to get \frac{243}{4}.

$$\frac{-\frac{9}{2}-\frac{243}{4}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

Subtract \frac{243}{4} from -\frac{9}{2} to get -\frac{261}{4}.

$$\frac{-\frac{261}{4}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

Divide -4 by 2 to get -2.

$$\frac{-\frac{261}{4}}{|-2\left(-\frac{1}{2}\right)^{2}|}$$

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

$$\frac{-\frac{261}{4}}{|-2\times \frac{1}{4}|}$$

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

$$\frac{-\frac{261}{4}}{|-\frac{1}{2}|}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{1}{2} is \frac{1}{2}.

$$\frac{-\frac{261}{4}}{\frac{1}{2}}$$

Divide -\frac{261}{4} by \frac{1}{2} by multiplying -\frac{261}{4} by the reciprocal of \frac{1}{2}.

$$-\frac{261}{4}\times 2$$

Multiply -\frac{261}{4} and 2 to get -\frac{261}{2}.

$$-\frac{261}{2}$$

Factor

$$-\frac{261}{2} = -130\frac{1}{2} = -130.5$$