Resolver (1-1/2)^2(-2)^3-3/2+|-(-1/6)^2+frac{1/4-frac{1}{5}}{(1-frac{2}{5})^2}|-frac{frac{1}{3}-frac{2}{9}}{frac{1}{8}-frac{15}{8}}=

$$( 1 - \frac { 1 } { 2 } ) ^ { 2 } ( - 2 ) ^ { 3 } - \frac { 3 } { 2 } + | - ( - \frac { 1 } { 6 } ) ^ { 2 } + \frac { \frac { 1 } { 4 } - \frac { 1 } { 5 } } { ( 1 - \frac { 2 } { 5 } ) ^ { 2 } } | - \frac { \frac { 1 } { 3 } - \frac { 2 } { 9 } } { \frac { 1 } { 8 } - \frac { 15 } { 8 } } =$$

Calcular

$$-\frac{419}{126}\approx -3.325396825$$

Pasos da solución

Resta \frac{1}{2} de 1 para obter \frac{1}{2}.

$$\left(\frac{1}{2}\right)^{2}\left(-2\right)^{3}-\frac{3}{2}+|-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Calcula \frac{1}{2} á potencia de 2 e obtén \frac{1}{4}.

$$\frac{1}{4}\left(-2\right)^{3}-\frac{3}{2}+|-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Calcula -2 á potencia de 3 e obtén -8.

$$\frac{1}{4}\left(-8\right)-\frac{3}{2}+|-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Multiplica \frac{1}{4} e -8 para obter -2.

$$-2-\frac{3}{2}+|-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Resta \frac{3}{2} de -2 para obter -\frac{7}{2}.

$$-\frac{7}{2}+|-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Calcula -\frac{1}{6} á potencia de 2 e obtén \frac{1}{36}.

$$-\frac{7}{2}+|-\frac{1}{36}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Resta \frac{1}{5} de \frac{1}{4} para obter \frac{1}{20}.

$$-\frac{7}{2}+|-\frac{1}{36}+\frac{\frac{1}{20}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Resta \frac{2}{5} de 1 para obter \frac{3}{5}.

$$-\frac{7}{2}+|-\frac{1}{36}+\frac{\frac{1}{20}}{\left(\frac{3}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Calcula \frac{3}{5} á potencia de 2 e obtén \frac{9}{25}.

$$-\frac{7}{2}+|-\frac{1}{36}+\frac{\frac{1}{20}}{\frac{9}{25}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Divide \frac{1}{20} entre \frac{9}{25} mediante a multiplicación de \frac{1}{20} polo recíproco de \frac{9}{25}.

$$-\frac{7}{2}+|-\frac{1}{36}+\frac{1}{20}\times \frac{25}{9}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Multiplica \frac{1}{20} e \frac{25}{9} para obter \frac{5}{36}.

$$-\frac{7}{2}+|-\frac{1}{36}+\frac{5}{36}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Suma -\frac{1}{36} e \frac{5}{36} para obter \frac{1}{9}.

$$-\frac{7}{2}+|\frac{1}{9}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

O valor absoluto dun número real a é a cando a\geq 0 ou -a cando a<0. O valor absoluto de \frac{1}{9} é \frac{1}{9}.

$$-\frac{7}{2}+\frac{1}{9}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Suma -\frac{7}{2} e \frac{1}{9} para obter -\frac{61}{18}.

$$-\frac{61}{18}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Resta \frac{2}{9} de \frac{1}{3} para obter \frac{1}{9}.

$$-\frac{61}{18}-\frac{\frac{1}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Resta \frac{15}{8} de \frac{1}{8} para obter -\frac{7}{4}.

$$-\frac{61}{18}-\frac{\frac{1}{9}}{-\frac{7}{4}}$$

Divide \frac{1}{9} entre -\frac{7}{4} mediante a multiplicación de \frac{1}{9} polo recíproco de -\frac{7}{4}.

$$-\frac{61}{18}-\frac{1}{9}\left(-\frac{4}{7}\right)$$

Multiplica \frac{1}{9} e -\frac{4}{7} para obter -\frac{4}{63}.

$$-\frac{61}{18}-\left(-\frac{4}{63}\right)$$

O contrario de -\frac{4}{63} é \frac{4}{63}.

$$-\frac{61}{18}+\frac{4}{63}$$

Suma -\frac{61}{18} e \frac{4}{63} para obter -\frac{419}{126}.

$$-\frac{419}{126}$$

Factorizar

$$-\frac{419}{126} = -3\frac{41}{126} = -3.3253968253968256$$