Solve sqrt{9/169}left(-2/5-2/3/frac{1{15}}right)-{left(-frac{4}{5}right)}^2

$$\sqrt{ \frac{ 9 }{ 169 } } \left( - \frac{ 2 }{ 5 } - \frac{ \frac{ 2 }{ 3 } }{ \frac{ 1 }{ 15 } } \right) - { \left(- \frac{ 4 }{ 5 } \right) }^{ 2 }$$

Evaluate

$$-\frac{76}{25}=-3.04$$

Solution Steps

Rewrite the square root of the division \frac{9}{169} as the division of square roots \frac{\sqrt{9}}{\sqrt{169}}. Take the square root of both numerator and denominator.

$$\frac{3}{13}\left(-\frac{2}{5}-\frac{\frac{2}{3}}{\frac{1}{15}}\right)-\left(-\frac{4}{5}\right)^{2}$$

Divide \frac{2}{3} by \frac{1}{15} by multiplying \frac{2}{3} by the reciprocal of \frac{1}{15}.

$$\frac{3}{13}\left(-\frac{2}{5}-\frac{2}{3}\times 15\right)-\left(-\frac{4}{5}\right)^{2}$$

Express \frac{2}{3}\times 15 as a single fraction.

$$\frac{3}{13}\left(-\frac{2}{5}-\frac{2\times 15}{3}\right)-\left(-\frac{4}{5}\right)^{2}$$

Multiply 2 and 15 to get 30.

$$\frac{3}{13}\left(-\frac{2}{5}-\frac{30}{3}\right)-\left(-\frac{4}{5}\right)^{2}$$

Divide 30 by 3 to get 10.

$$\frac{3}{13}\left(-\frac{2}{5}-10\right)-\left(-\frac{4}{5}\right)^{2}$$

Convert 10 to fraction \frac{50}{5}.

$$\frac{3}{13}\left(-\frac{2}{5}-\frac{50}{5}\right)-\left(-\frac{4}{5}\right)^{2}$$

Since -\frac{2}{5} and \frac{50}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{13}\times \frac{-2-50}{5}-\left(-\frac{4}{5}\right)^{2}$$

Subtract 50 from -2 to get -52.

$$\frac{3}{13}\left(-\frac{52}{5}\right)-\left(-\frac{4}{5}\right)^{2}$$

Multiply \frac{3}{13} times -\frac{52}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\left(-52\right)}{13\times 5}-\left(-\frac{4}{5}\right)^{2}$$

Do the multiplications in the fraction \frac{3\left(-52\right)}{13\times 5}.

$$\frac{-156}{65}-\left(-\frac{4}{5}\right)^{2}$$

Reduce the fraction \frac{-156}{65} to lowest terms by extracting and canceling out 13.

$$-\frac{12}{5}-\left(-\frac{4}{5}\right)^{2}$$

Calculate -\frac{4}{5} to the power of 2 and get \frac{16}{25}.

$$-\frac{12}{5}-\frac{16}{25}$$

Least common multiple of 5 and 25 is 25. Convert -\frac{12}{5} and \frac{16}{25} to fractions with denominator 25.

$$-\frac{60}{25}-\frac{16}{25}$$

Since -\frac{60}{25} and \frac{16}{25} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-60-16}{25}$$

Subtract 16 from -60 to get -76.

$$-\frac{76}{25}$$

Factor

$$-\frac{76}{25} = -3\frac{1}{25} = -3.04$$