Resolver {(1+3/4-1/2)^2:[1-(5/4-1/2)]^2*(frac{2}{5}:frac{5}{4})*frac{1}{14}}^2

$$\{ ( 1 + \frac { 3 } { 4 } - \frac { 1 } { 2 } ) ^ { 2 } : [ 1 - ( \frac { 5 } { 4 } - \frac { 1 } { 2 } ) ] ^ { 2 } \cdot ( \frac { 2 } { 5 } : \frac { 5 } { 4 } ) \cdot \frac { 1 } { 14 } \} ^ { 2 }$$

Calcular

$$\frac{16}{49}\approx 0.326530612$$

Pasos da solución

Suma 1 e \frac{3}{4} para obter \frac{7}{4}.

$$\left(\frac{\left(\frac{7}{4}-\frac{1}{2}\right)^{2}}{\left(1-\left(\frac{5}{4}-\frac{1}{2}\right)\right)^{2}}\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\right)^{2}$$

Resta \frac{1}{2} de \frac{7}{4} para obter \frac{5}{4}.

$$\left(\frac{\left(\frac{5}{4}\right)^{2}}{\left(1-\left(\frac{5}{4}-\frac{1}{2}\right)\right)^{2}}\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\right)^{2}$$

Calcula \frac{5}{4} á potencia de 2 e obtén \frac{25}{16}.

$$\left(\frac{\frac{25}{16}}{\left(1-\left(\frac{5}{4}-\frac{1}{2}\right)\right)^{2}}\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\right)^{2}$$

Resta \frac{1}{2} de \frac{5}{4} para obter \frac{3}{4}.

$$\left(\frac{\frac{25}{16}}{\left(1-\frac{3}{4}\right)^{2}}\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\right)^{2}$$

Resta \frac{3}{4} de 1 para obter \frac{1}{4}.

$$\left(\frac{\frac{25}{16}}{\left(\frac{1}{4}\right)^{2}}\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\right)^{2}$$

Calcula \frac{1}{4} á potencia de 2 e obtén \frac{1}{16}.

$$\left(\frac{\frac{25}{16}}{\frac{1}{16}}\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\right)^{2}$$

Divide \frac{25}{16} entre \frac{1}{16} mediante a multiplicación de \frac{25}{16} polo recíproco de \frac{1}{16}.

$$\left(\frac{25}{16}\times 16\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\right)^{2}$$

Multiplica \frac{25}{16} e 16 para obter 25.

$$\left(25\times \frac{\frac{2}{5}}{\frac{5}{4}}\times \frac{1}{14}\right)^{2}$$

Divide \frac{2}{5} entre \frac{5}{4} mediante a multiplicación de \frac{2}{5} polo recíproco de \frac{5}{4}.

$$\left(25\times \frac{2}{5}\times \frac{4}{5}\times \frac{1}{14}\right)^{2}$$

Multiplica \frac{2}{5} e \frac{4}{5} para obter \frac{8}{25}.

$$\left(25\times \frac{8}{25}\times \frac{1}{14}\right)^{2}$$

Multiplica 25 e \frac{8}{25} para obter 8.

$$\left(8\times \frac{1}{14}\right)^{2}$$

Multiplica 8 e \frac{1}{14} para obter \frac{4}{7}.

$$\left(\frac{4}{7}\right)^{2}$$

Calcula \frac{4}{7} á potencia de 2 e obtén \frac{16}{49}.

$$\frac{16}{49}$$

Factorizar

$$\frac{2 ^ {4}}{7 ^ {2}} = 0.32653061224489793$$