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

$$\frac { 2 } { 5 } \times \sqrt { \frac { 9 } { 16 } } \div ( - \frac { 1 } { 2 } ) ^ { 3 }$$

Evaluate

$$-\frac{12}{5}=-2.4$$

Solution Steps

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.

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

Multiply \frac{2}{5} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{2\times 3}{5\times 4}.

$$\frac{\frac{6}{20}}{\left(-\frac{1}{2}\right)^{3}}$$

Reduce the fraction \frac{6}{20} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{3}{10}}{\left(-\frac{1}{2}\right)^{3}}$$

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

$$\frac{\frac{3}{10}}{-\frac{1}{8}}$$

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

$$\frac{3}{10}\left(-8\right)$$

Express \frac{3}{10}\left(-8\right) as a single fraction.

$$\frac{3\left(-8\right)}{10}$$

Multiply 3 and -8 to get -24.

$$\frac{-24}{10}$$

Reduce the fraction \frac{-24}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{12}{5}$$

Factor

$$-\frac{12}{5} = -2\frac{2}{5} = -2.4$$