Solve [-2/9a^2(+3/5ab):(-1/3a+4/3a)]+(-frac{2}{3}a)(-frac{1}{5}ab)

$$[ - \frac { 2 } { 9 } a ^ { 2 } ( + \frac { 3 } { 5 } a b ) : ( - \frac { 1 } { 3 } a + \frac { 4 } { 3 } a ) ] + ( - \frac { 2 } { 3 } a ) ( - \frac { 1 } { 5 } a b )$$

Evaluate

$$0$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{-\frac{2}{9}a^{3}\times \frac{3}{5}b}{-\frac{1}{3}a+\frac{4}{3}a}-\frac{2}{3}a\left(-\frac{1}{5}\right)ab$$

Multiply a and a to get a^{2}.

$$\frac{-\frac{2}{9}a^{3}\times \frac{3}{5}b}{-\frac{1}{3}a+\frac{4}{3}a}-\frac{2}{3}a^{2}\left(-\frac{1}{5}\right)b$$

Multiply -\frac{2}{9} and \frac{3}{5} to get -\frac{2}{15}.

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

Combine -\frac{1}{3}a and \frac{4}{3}a to get a.

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

Cancel out a in both numerator and denominator.

$$-\frac{2}{15}ba^{2}-\frac{2}{3}a^{2}\left(-\frac{1}{5}\right)b$$

Multiply -\frac{2}{3} and -\frac{1}{5} to get \frac{2}{15}.

$$-\frac{2}{15}ba^{2}+\frac{2}{15}a^{2}b$$

Combine -\frac{2}{15}ba^{2} and \frac{2}{15}a^{2}b to get 0.

$$0$$

Factor

$$0$$