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}}

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

Avaliar

$$\frac{139}{24}\approx 5,791666667$$

Passos Para a Resolução

Calcule \sqrt[5]{\frac{1}{32}} e obtenha \frac{1}{2}.

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

Calcule \frac{2}{3} elevado a -1 e obtenha \frac{3}{2}.

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

Divida \frac{1}{2} por \frac{3}{2} ao multiplicar \frac{1}{2} pelo recíproco de \frac{3}{2}.

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

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

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

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

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

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

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

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

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

Expresse \frac{\frac{1}{3}}{2} como uma fração única.

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

Multiplique 3 e 2 para obter 6.

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

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

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

Reescreva a raiz quadrada da divisão \frac{9}{25} à medida que a divisão de raízes quadradas \frac{\sqrt{9}}{\sqrt{25}}. Calcule a raiz quadrada do numerador e do denominador.

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

Calcule \frac{15}{2} elevado a 1 e obtenha \frac{15}{2}.

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

Divida \frac{4}{5} por \frac{15}{2} ao multiplicar \frac{4}{5} pelo recíproco de \frac{15}{2}.

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

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

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

Divida \frac{3}{5} por \frac{8}{75} ao multiplicar \frac{3}{5} pelo recíproco de \frac{8}{75}.

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

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

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

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

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

Fatorizar

$$\frac{139}{2 ^ {3} \cdot 3} = 5\frac{19}{24} = 5,791666666666667$$