Resolver frac{sqrt[5]{frac{1/32}}{{left(2/3right)}^-1}}{left(1-1/3right)9/4+frac{1}{2}}+frac{sqrt{1-frac{16}{25}}}{frac{frac{4}{5}}{{left(frac{15}{2}right)}^1}}

$$\frac{ \frac{ \sqrt[ 5 ]{ \frac{ 1 }{ 32 } } }{ { \left( \frac{ 2 }{ 3 } \right) }^{ -1 } } }{ \left( 1- \frac{ 1 }{ 3 } \right) \frac{ 9 }{ 4 } + \frac{ 1 }{ 2 } } + \frac{ \sqrt{ 1- \frac{ 16 }{ 25 } } }{ \frac{ \frac{ 4 }{ 5 } }{ { \left( \frac{ 15 }{ 2 } \right) }^{ 1 } } }$$

Calcular

$$\frac{139}{24}\approx 5.791666667$$

Pasos da solución

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

$$\frac{\frac{\frac{1}{2}}{\left(\frac{2}{3}\right)^{-1}}}{\left(1-\frac{1}{3}\right)\times \frac{9}{4}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

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

$$\frac{\frac{\frac{1}{2}}{\frac{3}{2}}}{\left(1-\frac{1}{3}\right)\times \frac{9}{4}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

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

$$\frac{\frac{1}{2}\times \frac{2}{3}}{\left(1-\frac{1}{3}\right)\times \frac{9}{4}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

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

$$\frac{\frac{1}{3}}{\left(1-\frac{1}{3}\right)\times \frac{9}{4}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

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

$$\frac{\frac{1}{3}}{\frac{2}{3}\times \frac{9}{4}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

Multiplica \frac{2}{3} e \frac{9}{4} para obter \frac{3}{2}.

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

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

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

Expresa \frac{\frac{1}{3}}{2} como unha única fracción.

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

Multiplica 3 e 2 para obter 6.

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

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

$$\frac{1}{6}+\frac{\sqrt{\frac{9}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

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.

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

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

$$\frac{1}{6}+\frac{\frac{3}{5}}{\frac{\frac{4}{5}}{\frac{15}{2}}}$$

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

$$\frac{1}{6}+\frac{\frac{3}{5}}{\frac{4}{5}\times \frac{2}{15}}$$

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

$$\frac{1}{6}+\frac{\frac{3}{5}}{\frac{8}{75}}$$

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

$$\frac{1}{6}+\frac{3}{5}\times \frac{75}{8}$$

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

$$\frac{1}{6}+\frac{45}{8}$$

Suma \frac{1}{6} e \frac{45}{8} para obter \frac{139}{24}.

$$\frac{139}{24}$$

Factorizar

$$\frac{139}{2 ^ {3} \cdot 3} = 5\frac{19}{24} = 5.791666666666667$$