Resolver sqrt[5]{frac{1/32}:(2/3)^-1}{(1-1/3)2/4+frac{1}{2}}+frac{sqrt{1-frac{16}{25}}}{frac{4}{5}:(frac{15}{2})^1}=

$$\frac { \sqrt[ 5 ] { \frac { 1 } { 32 } } : ( \frac { 2 } { 3 } ) ^ { - 1 } } { ( 1 - \frac { 1 } { 3 } ) \frac { 2 } { 4 } + \frac { 1 } { 2 } } + \frac { \sqrt { 1 - \frac { 16 } { 25 } } } { \frac { 4 } { 5 } : ( \frac { 15 } { 2 } ) ^ { 1 } } =$$

Calcular

$$\frac{241}{40}=6.025$$

Pasos da solución

Calcular \sqrt[5]{\frac{1}{32}} e obter \frac{1}{2}.

$$\frac{\frac{\frac{1}{2}}{\left(\frac{2}{3}\right)^{-1}}}{\left(1-\frac{1}{3}\right)\times \frac{2}{4}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

Calcula \frac{2}{3} á potencia de -1 e obtén \frac{3}{2}.

$$\frac{\frac{\frac{1}{2}}{\frac{3}{2}}}{\left(1-\frac{1}{3}\right)\times \frac{2}{4}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

Divide \frac{1}{2} entre \frac{3}{2} mediante a multiplicación de \frac{1}{2} polo recíproco de \frac{3}{2}.

$$\frac{\frac{1}{2}\times \frac{2}{3}}{\left(1-\frac{1}{3}\right)\times \frac{2}{4}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

Multiplica \frac{1}{2} e \frac{2}{3} para obter \frac{1}{3}.

$$\frac{\frac{1}{3}}{\left(1-\frac{1}{3}\right)\times \frac{2}{4}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

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

$$\frac{\frac{1}{3}}{\frac{2}{3}\times \frac{2}{4}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

Reduce a fracción \frac{2}{4} a termos máis baixos extraendo e cancelando 2.

$$\frac{\frac{1}{3}}{\frac{2}{3}\times \frac{1}{2}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

Multiplica \frac{2}{3} e \frac{1}{2} para obter \frac{1}{3}.

$$\frac{\frac{1}{3}}{\frac{1}{3}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

Suma \frac{1}{3} e \frac{1}{2} para obter \frac{5}{6}.

$$\frac{\frac{1}{3}}{\frac{5}{6}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

Divide \frac{1}{3} entre \frac{5}{6} mediante a multiplicación de \frac{1}{3} polo recíproco de \frac{5}{6}.

$$\frac{1}{3}\times \frac{6}{5}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

Multiplica \frac{1}{3} e \frac{6}{5} para obter \frac{2}{5}.

$$\frac{2}{5}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

Resta \frac{16}{25} de 1 para obter \frac{9}{25}.

$$\frac{2}{5}+\frac{\sqrt{\frac{9}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

Reescribe a raíz cadrada da división \frac{9}{25} como a división de raíces cadradas \frac{\sqrt{9}}{\sqrt{25}}. Obtén a raíz cadrada do numerador e o denominador.

$$\frac{2}{5}+\frac{\frac{3}{5}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

Calcula \frac{15}{2} á potencia de 1 e obtén \frac{15}{2}.

$$\frac{2}{5}+\frac{\frac{3}{5}}{\frac{\frac{4}{5}}{\frac{15}{2}}}$$

Divide \frac{4}{5} entre \frac{15}{2} mediante a multiplicación de \frac{4}{5} polo recíproco de \frac{15}{2}.

$$\frac{2}{5}+\frac{\frac{3}{5}}{\frac{4}{5}\times \frac{2}{15}}$$

Multiplica \frac{4}{5} e \frac{2}{15} para obter \frac{8}{75}.

$$\frac{2}{5}+\frac{\frac{3}{5}}{\frac{8}{75}}$$

Divide \frac{3}{5} entre \frac{8}{75} mediante a multiplicación de \frac{3}{5} polo recíproco de \frac{8}{75}.

$$\frac{2}{5}+\frac{3}{5}\times \frac{75}{8}$$

Multiplica \frac{3}{5} e \frac{75}{8} para obter \frac{45}{8}.

$$\frac{2}{5}+\frac{45}{8}$$

Suma \frac{2}{5} e \frac{45}{8} para obter \frac{241}{40}.

$$\frac{241}{40}$$

Factorizar

$$\frac{241}{2 ^ {3} \cdot 5} = 6\frac{1}{40} = 6.025$$