Solve 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}=

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

Evaluate

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

Solution Steps

Calculate \sqrt[5]{\frac{1}{32}} and get \frac{1}{2}.

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

Calculate \frac{2}{3} to the power of -1 and get \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} by \frac{3}{2} by multiplying \frac{1}{2} by the reciprocal of \frac{3}{2}.

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

Multiply \frac{1}{2} and \frac{2}{3} to get \frac{1}{3}.

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

Subtract \frac{1}{3} from 1 to get \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 the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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

Multiply \frac{2}{3} and \frac{1}{2} to get \frac{1}{3}.

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

Add \frac{1}{3} and \frac{1}{2} to get \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} by \frac{5}{6} by multiplying \frac{1}{3} by the reciprocal of \frac{5}{6}.

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

Multiply \frac{1}{3} and \frac{6}{5} to get \frac{2}{5}.

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

Subtract \frac{16}{25} from 1 to get \frac{9}{25}.

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

Rewrite the square root of the division \frac{9}{25} as the division of square roots \frac{\sqrt{9}}{\sqrt{25}}. Take the square root of both numerator and denominator.

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

Calculate \frac{15}{2} to the power of 1 and get \frac{15}{2}.

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

Divide \frac{4}{5} by \frac{15}{2} by multiplying \frac{4}{5} by the reciprocal of \frac{15}{2}.

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

Multiply \frac{4}{5} and \frac{2}{15} to get \frac{8}{75}.

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

Divide \frac{3}{5} by \frac{8}{75} by multiplying \frac{3}{5} by the reciprocal of \frac{8}{75}.

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

Multiply \frac{3}{5} and \frac{75}{8} to get \frac{45}{8}.

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

Add \frac{2}{5} and \frac{45}{8} to get \frac{241}{40}.

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

Factor

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