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

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

Avaliar

$$-\frac{261}{2}=-130,5$$

Passos Para a Resolução

Calcule -1 elevado a 3 e obtenha -1.

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

Divida -1 por \frac{2}{9} ao multiplicar -1 pelo recíproco de \frac{2}{9}.

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

Calcule 2 elevado a 200 e obtenha 1606938044258990275541962092341162602522202993782792835301376.

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

Multiplique 0 e 5 para obter 0.

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

Calcule 0 elevado a 200 e obtenha 0.

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

Multiplique 1606938044258990275541962092341162602522202993782792835301376 e 0 para obter 0.

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

Some -\frac{9}{2} e 0 para obter -\frac{9}{2}.

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

Calcule 3 elevado a 3 e obtenha 27.

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

Calcule -\frac{3}{2} elevado a 2 e obtenha \frac{9}{4}.

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

Multiplique 27 e \frac{9}{4} para obter \frac{243}{4}.

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

Subtraia \frac{243}{4} de -\frac{9}{2} para obter -\frac{261}{4}.

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

Dividir -4 por 2 para obter -2.

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

Calcule -\frac{1}{2} elevado a 2 e obtenha \frac{1}{4}.

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

Multiplique -2 e \frac{1}{4} para obter -\frac{1}{2}.

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

O valor absoluto de um número real a é a quando a\geq 0 ou -a quando a<0. O valor absoluto de -\frac{1}{2} é \frac{1}{2}.

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

Divida -\frac{261}{4} por \frac{1}{2} ao multiplicar -\frac{261}{4} pelo recíproco de \frac{1}{2}.

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

Multiplique -\frac{261}{4} e 2 para obter -\frac{261}{2}.

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

Fatorizar

$$-\frac{261}{2} = -130\frac{1}{2} = -130,5$$