Solve ab^2div(-1/3ab)*2a^2b

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

Evaluate

$$-6\left(ab\right)^{2}$$

Solution Steps

Cancel out ab in both numerator and denominator.

$$\frac{b}{-\frac{1}{3}}\times 2a^{2}b$$

Divide b by -\frac{1}{3} by multiplying b by the reciprocal of -\frac{1}{3}.

$$\frac{b\times 3}{-1}\times 2a^{2}b$$

Anything divided by -1 gives its opposite.

$$\left(-b\times 3\right)\times 2a^{2}b$$

Multiply -1 and 3 to get -3.

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

Multiply -3 and 2 to get -6.

$$-6ba^{2}b$$

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

$$-6b^{2}a^{2}$$

Differentiate w.r.t. a

$$-12ab^{2}$$