Solve |2*(-2/5)div(-11/4)|-3^2*(-2/3)^2

$$| 2 \times ( - \frac { 2 } { 5 } ) \div ( - 1 \frac { 1 } { 4 } ) | - 3 ^ { 2 } \times ( - \frac { 2 } { 3 } ) ^ { 2 }$$

Evaluate

$$-\frac{84}{25}=-3.36$$

Solution Steps

Express 2\left(-\frac{2}{5}\right) as a single fraction.

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

Multiply 2 and -2 to get -4.

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

Fraction \frac{-4}{5} can be rewritten as -\frac{4}{5} by extracting the negative sign.

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

Multiply 1 and 4 to get 4.

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

Add 4 and 1 to get 5.

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

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

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

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

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

Do the multiplications in the fraction \frac{-4\left(-4\right)}{5\times 5}.

$$|\frac{16}{25}|-3^{2}\left(-\frac{2}{3}\right)^{2}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of \frac{16}{25} is \frac{16}{25}.

$$\frac{16}{25}-3^{2}\left(-\frac{2}{3}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{16}{25}-9\left(-\frac{2}{3}\right)^{2}$$

Calculate -\frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$\frac{16}{25}-9\times \frac{4}{9}$$

Cancel out 9 and 9.

$$\frac{16}{25}-4$$

Convert 4 to fraction \frac{100}{25}.

$$\frac{16}{25}-\frac{100}{25}$$

Since \frac{16}{25} and \frac{100}{25} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16-100}{25}$$

Subtract 100 from 16 to get -84.

$$-\frac{84}{25}$$

Factor

$$-\frac{84}{25} = -3\frac{9}{25} = -3.36$$