Solve [(-1)^{3}div2/9+2^{200}*(-0.5)^200-3^3*(-3/2)^2]div|-4div2*(-1/2)^2|

$$[ ( - 1 ) ^ { 3 } \div \frac { 2 } { 9 } + 2 ^ { 200 } \times ( - 0.5 ) ^ { 200 } - 3 ^ { 3 } \times ( - \frac { 3 } { 2 } ) ^ { 2 } ] \div | - 4 \div 2 \times ( - \frac { 1 } { 2 } ) ^ { 2 } |$$

Evaluate

$$-128.5$$

Solution Steps

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

$$\frac{\frac{-1}{\frac{2}{9}}+2^{200}\left(-0.5\right)^{200}-3^{3}\left(-\frac{3}{2}\right)^{2}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

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

$$\frac{-\frac{9}{2}+2^{200}\left(-0.5\right)^{200}-3^{3}\left(-\frac{3}{2}\right)^{2}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

Calculate 2 to the power of 200 and get 1606938044258990275541962092341162602522202993782792835301376.

$$\frac{-\frac{9}{2}+1606938044258990275541962092341162602522202993782792835301376\left(-0.5\right)^{200}-3^{3}\left(-\frac{3}{2}\right)^{2}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

Calculate -0.5 to the power of 200 and get 0.00000000000000000000000000000000000000000000000000000000000062230152778611417071440640537801242405902521687211671331011166147896988340353834411839448231257136169569665895551224821247160434722900390625.

$$\frac{-\frac{9}{2}+1606938044258990275541962092341162602522202993782792835301376\times 0.00000000000000000000000000000000000000000000000000000000000062230152778611417071440640537801242405902521687211671331011166147896988340353834411839448231257136169569665895551224821247160434722900390625-3^{3}\left(-\frac{3}{2}\right)^{2}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

Multiply 1606938044258990275541962092341162602522202993782792835301376 and 0.00000000000000000000000000000000000000000000000000000000000062230152778611417071440640537801242405902521687211671331011166147896988340353834411839448231257136169569665895551224821247160434722900390625 to get 1.

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

Convert 1 to fraction \frac{2}{2}.

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

Since -\frac{9}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

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

Add -9 and 2 to get -7.

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

Calculate 3 to the power of 3 and get 27.

$$\frac{-\frac{7}{2}-27\left(-\frac{3}{2}\right)^{2}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

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

$$\frac{-\frac{7}{2}-27\times \frac{9}{4}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

Express 27\times \frac{9}{4} as a single fraction.

$$\frac{-\frac{7}{2}-\frac{27\times 9}{4}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

Multiply 27 and 9 to get 243.

$$\frac{-\frac{7}{2}-\frac{243}{4}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

Least common multiple of 2 and 4 is 4. Convert -\frac{7}{2} and \frac{243}{4} to fractions with denominator 4.

$$\frac{-\frac{14}{4}-\frac{243}{4}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

Since -\frac{14}{4} and \frac{243}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-14-243}{4}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

Subtract 243 from -14 to get -257.

$$\frac{-\frac{257}{4}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

Divide -4 by 2 to get -2.

$$\frac{-\frac{257}{4}}{|-2\left(-\frac{1}{2}\right)^{2}|}$$

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

$$\frac{-\frac{257}{4}}{|-2\times \frac{1}{4}|}$$

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

$$\frac{-\frac{257}{4}}{|\frac{-2}{4}|}$$

Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{257}{4}}{|-\frac{1}{2}|}$$

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}.

$$\frac{-\frac{257}{4}}{\frac{1}{2}}$$

Divide -\frac{257}{4} by \frac{1}{2} by multiplying -\frac{257}{4} by the reciprocal of \frac{1}{2}.

$$-\frac{257}{4}\times 2$$

Express -\frac{257}{4}\times 2 as a single fraction.

$$\frac{-257\times 2}{4}$$

Multiply -257 and 2 to get -514.

$$\frac{-514}{4}$$

Reduce the fraction \frac{-514}{4} to lowest terms by extracting and canceling out 2.

$$-\frac{257}{2}$$

Factor

$$-128.5$$