Solve 3/2adiv6/5b*(-4ab)

$$\frac { 3 } { 2 } a \div \frac { 6 } { 5 } b \times ( - 4 a b )$$

Evaluate

$$-5\left(ab\right)^{2}$$

Solution Steps

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

$$\frac{\frac{3}{2}a}{\frac{6}{5}}b^{2}\left(-4\right)a$$

Divide \frac{3}{2}a by \frac{6}{5} by multiplying \frac{3}{2}a by the reciprocal of \frac{6}{5}.

$$\frac{\frac{3}{2}a\times 5}{6}b^{2}\left(-4\right)a$$

Express \frac{3}{2}\times 5 as a single fraction.

$$\frac{\frac{3\times 5}{2}a}{6}b^{2}\left(-4\right)a$$

Multiply 3 and 5 to get 15.

$$\frac{\frac{15}{2}a}{6}b^{2}\left(-4\right)a$$

Divide \frac{15}{2}a by 6 to get \frac{5}{4}a.

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

Express \frac{5}{4}\left(-4\right) as a single fraction.

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

Multiply 5 and -4 to get -20.

$$\frac{-20}{4}ab^{2}a$$

Divide -20 by 4 to get -5.

$$-5ab^{2}a$$

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

$$-5a^{2}b^{2}$$

Differentiate w.r.t. a

$$-10ab^{2}$$