Solve -1/2ab*(-4a)div2/3ab

$$- \frac { 1 } { 2 } a b \times ( - 4 a ) \div \frac { 2 } { 3 } a b$$

Evaluate

$$3b^{2}a^{3}$$

Solution Steps

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

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

Express -\frac{1}{2}\left(-4\right) as a single fraction.

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

Multiply -1 and -4 to get 4.

$$\frac{\frac{4}{2}a^{2}b}{\frac{2}{3}}ab$$

Divide 4 by 2 to get 2.

$$\frac{2a^{2}b}{\frac{2}{3}}ab$$

Divide 2a^{2}b by \frac{2}{3} by multiplying 2a^{2}b by the reciprocal of \frac{2}{3}.

$$\frac{2a^{2}b\times 3}{2}ab$$

Cancel out 2 and 2.

$$a^{2}b\times 3ab$$

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

$$a^{3}b\times 3b$$

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

$$a^{3}b^{2}\times 3$$

Differentiate w.r.t. b

$$6ba^{3}$$