Solve {l}{2/5*sqrt{9/16}div(-1/2)^3}{3/5*(-frac{2}{2})^3*(frac{3}{5})}

$$\left. \begin{array} { l } { \frac { 2 } { 5 } \times \sqrt { \frac { 9 } { 16 } } \div ( - \frac { 1 } { 2 } ) ^ { 3 } } \\ { \frac { 3 } { 5 } \times ( - \frac { 2 } { 2 } ) ^ { 3 } \times ( \frac { 3 } { 5 } ) } \end{array} \right.$$

Sort

$$-\frac{12}{5},\ -\frac{9}{25}$$

Solution Steps

Divide 2 by 2 to get 1.

$$sort(\frac{\frac{2}{5}\sqrt{\frac{9}{16}}}{\left(-\frac{1}{2}\right)^{3}},\frac{3}{5}\left(-1\right)^{3}\times \frac{3}{5})$$

Rewrite the square root of the division \frac{9}{16} as the division of square roots \frac{\sqrt{9}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$sort(\frac{\frac{2}{5}\times \frac{3}{4}}{\left(-\frac{1}{2}\right)^{3}},\frac{3}{5}\left(-1\right)^{3}\times \frac{3}{5})$$

Multiply \frac{2}{5} and \frac{3}{4} to get \frac{3}{10}.

$$sort(\frac{\frac{3}{10}}{\left(-\frac{1}{2}\right)^{3}},\frac{3}{5}\left(-1\right)^{3}\times \frac{3}{5})$$

Calculate -\frac{1}{2} to the power of 3 and get -\frac{1}{8}.

$$sort(\frac{\frac{3}{10}}{-\frac{1}{8}},\frac{3}{5}\left(-1\right)^{3}\times \frac{3}{5})$$

Divide \frac{3}{10} by -\frac{1}{8} by multiplying \frac{3}{10} by the reciprocal of -\frac{1}{8}.

$$sort(\frac{3}{10}\left(-8\right),\frac{3}{5}\left(-1\right)^{3}\times \frac{3}{5})$$

Multiply \frac{3}{10} and -8 to get -\frac{12}{5}.

$$sort(-\frac{12}{5},\frac{3}{5}\left(-1\right)^{3}\times \frac{3}{5})$$

Calculate -1 to the power of 3 and get -1.

$$sort(-\frac{12}{5},\frac{3}{5}\left(-1\right)\times \frac{3}{5})$$

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

$$sort(-\frac{12}{5},-\frac{3}{5}\times \frac{3}{5})$$

Multiply -\frac{3}{5} and \frac{3}{5} to get -\frac{9}{25}.

$$sort(-\frac{12}{5},-\frac{9}{25})$$

Least common denominator of the numbers in the list -\frac{12}{5},-\frac{9}{25} is 25. Convert numbers in the list to fractions with denominator 25.

$$-\frac{60}{25},-\frac{9}{25}$$

Evaluate

$$-\frac{12}{5},\ -\frac{9}{25}$$