Solve (-2/3a^{7}b^{6}):(4/15a^5b^5)-2a^2b+(3ab)[-2a+3(4a)]+3/2a^2b

$$( - \frac { 2 } { 3 } a ^ { 7 } b ^ { 6 } ) : ( \frac { 4 } { 15 } a ^ { 5 } b ^ { 5 } ) - 2 a ^ { 2 } b + ( 3 a b ) [ - 2 a + 3 ( 4 a ) ] + \frac { 3 } { 2 } a ^ { 2 } b$$

Evaluate

$$27ba^{2}$$

Solution Steps

Cancel out a^{5}b^{5} in both numerator and denominator.

$$\frac{-\frac{2}{3}ba^{2}}{\frac{4}{15}}-2a^{2}b+3ab\left(-2a+3\times 4a\right)+\frac{3}{2}a^{2}b$$

Divide -\frac{2}{3}ba^{2} by \frac{4}{15} by multiplying -\frac{2}{3}ba^{2} by the reciprocal of \frac{4}{15}.

$$\frac{-\frac{2}{3}ba^{2}\times 15}{4}-2a^{2}b+3ab\left(-2a+3\times 4a\right)+\frac{3}{2}a^{2}b$$

Multiply -\frac{2}{3} and 15 to get -10.

$$\frac{-10ba^{2}}{4}-2a^{2}b+3ab\left(-2a+3\times 4a\right)+\frac{3}{2}a^{2}b$$

Divide -10ba^{2} by 4 to get -\frac{5}{2}ba^{2}.

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

Combine -\frac{5}{2}ba^{2} and -2a^{2}b to get -\frac{9}{2}ba^{2}.

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

Multiply 3 and 4 to get 12.

$$-\frac{9}{2}ba^{2}+3ab\left(-2a+12a\right)+\frac{3}{2}a^{2}b$$

Combine -2a and 12a to get 10a.

$$-\frac{9}{2}ba^{2}+3ab\times 10a+\frac{3}{2}a^{2}b$$

Multiply 3 and 10 to get 30.

$$-\frac{9}{2}ba^{2}+30aba+\frac{3}{2}a^{2}b$$

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

$$-\frac{9}{2}ba^{2}+30a^{2}b+\frac{3}{2}a^{2}b$$

Combine -\frac{9}{2}ba^{2} and 30a^{2}b to get \frac{51}{2}ba^{2}.

$$\frac{51}{2}ba^{2}+\frac{3}{2}a^{2}b$$

Combine \frac{51}{2}ba^{2} and \frac{3}{2}a^{2}b to get 27ba^{2}.

$$27ba^{2}$$

Expand

$$27ba^{2}$$

Solution Steps

Cancel out a^{5}b^{5} in both numerator and denominator.

$$\frac{-\frac{2}{3}ba^{2}}{\frac{4}{15}}-2a^{2}b+3ab\left(-2a+3\times 4a\right)+\frac{3}{2}a^{2}b$$

Divide -\frac{2}{3}ba^{2} by \frac{4}{15} by multiplying -\frac{2}{3}ba^{2} by the reciprocal of \frac{4}{15}.

$$\frac{-\frac{2}{3}ba^{2}\times 15}{4}-2a^{2}b+3ab\left(-2a+3\times 4a\right)+\frac{3}{2}a^{2}b$$

Multiply -\frac{2}{3} and 15 to get -10.

$$\frac{-10ba^{2}}{4}-2a^{2}b+3ab\left(-2a+3\times 4a\right)+\frac{3}{2}a^{2}b$$

Divide -10ba^{2} by 4 to get -\frac{5}{2}ba^{2}.

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

Combine -\frac{5}{2}ba^{2} and -2a^{2}b to get -\frac{9}{2}ba^{2}.

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

Multiply 3 and 4 to get 12.

$$-\frac{9}{2}ba^{2}+3ab\left(-2a+12a\right)+\frac{3}{2}a^{2}b$$

Combine -2a and 12a to get 10a.

$$-\frac{9}{2}ba^{2}+3ab\times 10a+\frac{3}{2}a^{2}b$$

Multiply 3 and 10 to get 30.

$$-\frac{9}{2}ba^{2}+30aba+\frac{3}{2}a^{2}b$$

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

$$-\frac{9}{2}ba^{2}+30a^{2}b+\frac{3}{2}a^{2}b$$

Combine -\frac{9}{2}ba^{2} and 30a^{2}b to get \frac{51}{2}ba^{2}.

$$\frac{51}{2}ba^{2}+\frac{3}{2}a^{2}b$$

Combine \frac{51}{2}ba^{2} and \frac{3}{2}a^{2}b to get 27ba^{2}.

$$27ba^{2}$$