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}=

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

Avaliar

$$\frac{241}{40}=6,025$$

Passos Para a Resolução

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

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

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

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

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

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

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

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

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

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

Reduza a fração \frac{2}{4} para os termos mais baixos ao retirar e anular 2.

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

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

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

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

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

Divida \frac{1}{3} por \frac{5}{6} ao multiplicar \frac{1}{3} pelo recíproco de \frac{5}{6}.

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

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

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

Fatorizar

$$\frac{241}{2 ^ {3} \cdot 5} = 6\frac{1}{40} = 6,025$$