Resolver (2-1/5)^2/(3-frac{4{4})^-1}+(6/7*frac{5/4-frac{1}{7}+frac{1}{2})^3}{(frac{1}{2}-frac{1}{3}*frac{1}{4}div5)}-4frac{4}{6}

$$\frac { ( 2 - \frac { 1 } { 5 } ) ^ { 2 } } { ( 3 - \frac { 4 } { 4 } ) ^ { - 1 } } + \frac { ( \frac { 6 } { 7 } \times \frac { 5 } { 4 } - \frac { 1 } { 7 } + \frac { 1 } { 2 } ) ^ { 3 } } { ( \frac { 1 } { 2 } - \frac { 1 } { 3 } \times \frac { 1 } { 4 } \div 5 ) } - 4 \frac { 4 } { 6 }$$

Calcular

$$\frac{5852792}{746025}\approx 7.845302771$$

Pasos da solución

Divide 4 entre 4 para obter 1.

$$\frac{\left(2-\frac{1}{5}\right)^{2}}{\left(3-1\right)^{-1}}+\frac{\left(\frac{6}{7}\times \frac{5}{4}-\frac{1}{7}+\frac{1}{2}\right)^{3}}{\frac{1}{2}-\frac{\frac{1}{3}\times \frac{1}{4}}{5}}-\frac{4\times 6+4}{6}$$

Resta \frac{1}{5} de 2 para obter \frac{9}{5}.

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

Calcula \frac{9}{5} á potencia de 2 e obtén \frac{81}{25}.

$$\frac{\frac{81}{25}}{\left(3-1\right)^{-1}}+\frac{\left(\frac{6}{7}\times \frac{5}{4}-\frac{1}{7}+\frac{1}{2}\right)^{3}}{\frac{1}{2}-\frac{\frac{1}{3}\times \frac{1}{4}}{5}}-\frac{4\times 6+4}{6}$$

Resta 1 de 3 para obter 2.

$$\frac{\frac{81}{25}}{2^{-1}}+\frac{\left(\frac{6}{7}\times \frac{5}{4}-\frac{1}{7}+\frac{1}{2}\right)^{3}}{\frac{1}{2}-\frac{\frac{1}{3}\times \frac{1}{4}}{5}}-\frac{4\times 6+4}{6}$$

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

$$\frac{\frac{81}{25}}{\frac{1}{2}}+\frac{\left(\frac{6}{7}\times \frac{5}{4}-\frac{1}{7}+\frac{1}{2}\right)^{3}}{\frac{1}{2}-\frac{\frac{1}{3}\times \frac{1}{4}}{5}}-\frac{4\times 6+4}{6}$$

Divide \frac{81}{25} entre \frac{1}{2} mediante a multiplicación de \frac{81}{25} polo recíproco de \frac{1}{2}.

$$\frac{81}{25}\times 2+\frac{\left(\frac{6}{7}\times \frac{5}{4}-\frac{1}{7}+\frac{1}{2}\right)^{3}}{\frac{1}{2}-\frac{\frac{1}{3}\times \frac{1}{4}}{5}}-\frac{4\times 6+4}{6}$$

Multiplica \frac{81}{25} e 2 para obter \frac{162}{25}.

$$\frac{162}{25}+\frac{\left(\frac{6}{7}\times \frac{5}{4}-\frac{1}{7}+\frac{1}{2}\right)^{3}}{\frac{1}{2}-\frac{\frac{1}{3}\times \frac{1}{4}}{5}}-\frac{4\times 6+4}{6}$$

Multiplica \frac{6}{7} e \frac{5}{4} para obter \frac{15}{14}.

$$\frac{162}{25}+\frac{\left(\frac{15}{14}-\frac{1}{7}+\frac{1}{2}\right)^{3}}{\frac{1}{2}-\frac{\frac{1}{3}\times \frac{1}{4}}{5}}-\frac{4\times 6+4}{6}$$

Resta \frac{1}{7} de \frac{15}{14} para obter \frac{13}{14}.

$$\frac{162}{25}+\frac{\left(\frac{13}{14}+\frac{1}{2}\right)^{3}}{\frac{1}{2}-\frac{\frac{1}{3}\times \frac{1}{4}}{5}}-\frac{4\times 6+4}{6}$$

Suma \frac{13}{14} e \frac{1}{2} para obter \frac{10}{7}.

$$\frac{162}{25}+\frac{\left(\frac{10}{7}\right)^{3}}{\frac{1}{2}-\frac{\frac{1}{3}\times \frac{1}{4}}{5}}-\frac{4\times 6+4}{6}$$

Calcula \frac{10}{7} á potencia de 3 e obtén \frac{1000}{343}.

$$\frac{162}{25}+\frac{\frac{1000}{343}}{\frac{1}{2}-\frac{\frac{1}{3}\times \frac{1}{4}}{5}}-\frac{4\times 6+4}{6}$$

Multiplica \frac{1}{3} e \frac{1}{4} para obter \frac{1}{12}.

$$\frac{162}{25}+\frac{\frac{1000}{343}}{\frac{1}{2}-\frac{\frac{1}{12}}{5}}-\frac{4\times 6+4}{6}$$

Expresa \frac{\frac{1}{12}}{5} como unha única fracción.

$$\frac{162}{25}+\frac{\frac{1000}{343}}{\frac{1}{2}-\frac{1}{12\times 5}}-\frac{4\times 6+4}{6}$$

Multiplica 12 e 5 para obter 60.

$$\frac{162}{25}+\frac{\frac{1000}{343}}{\frac{1}{2}-\frac{1}{60}}-\frac{4\times 6+4}{6}$$

Resta \frac{1}{60} de \frac{1}{2} para obter \frac{29}{60}.

$$\frac{162}{25}+\frac{\frac{1000}{343}}{\frac{29}{60}}-\frac{4\times 6+4}{6}$$

Divide \frac{1000}{343} entre \frac{29}{60} mediante a multiplicación de \frac{1000}{343} polo recíproco de \frac{29}{60}.

$$\frac{162}{25}+\frac{1000}{343}\times \frac{60}{29}-\frac{4\times 6+4}{6}$$

Multiplica \frac{1000}{343} e \frac{60}{29} para obter \frac{60000}{9947}.

$$\frac{162}{25}+\frac{60000}{9947}-\frac{4\times 6+4}{6}$$

Suma \frac{162}{25} e \frac{60000}{9947} para obter \frac{3111414}{248675}.

$$\frac{3111414}{248675}-\frac{4\times 6+4}{6}$$

Multiplica 4 e 6 para obter 24.

$$\frac{3111414}{248675}-\frac{24+4}{6}$$

Suma 24 e 4 para obter 28.

$$\frac{3111414}{248675}-\frac{28}{6}$$

Reduce a fracción \frac{28}{6} a termos máis baixos extraendo e cancelando 2.

$$\frac{3111414}{248675}-\frac{14}{3}$$

Resta \frac{14}{3} de \frac{3111414}{248675} para obter \frac{5852792}{746025}.

$$\frac{5852792}{746025}$$

Factorizar

$$\frac{2 ^ {3} \cdot 11 \cdot 66509}{3 \cdot 5 ^ {2} \cdot 7 ^ {3} \cdot 29} = 7\frac{630617}{746025} = 7.845302771354848$$