Solve 2a^2b/a^2b^3:-2ab/3a^5=

$$\frac { 2 a ^ { 2 } b } { a ^ { 2 } b ^ { 3 } } : \frac { - 2 a b } { 3 a ^ { 5 } } =$$

Evaluate

$$-\frac{3a^{4}}{b^{3}}$$

Solution Steps

Divide \frac{2a^{2}b}{a^{2}b^{3}} by \frac{-2ab}{3a^{5}} by multiplying \frac{2a^{2}b}{a^{2}b^{3}} by the reciprocal of \frac{-2ab}{3a^{5}}.

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

Cancel out 2aba^{2} in both numerator and denominator.

$$\frac{3a^{4}}{-bb^{2}}$$

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

$$\frac{3a^{4}}{-b^{3}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{-3a^{4}}{b^{3}}$$

Differentiate w.r.t. a

$$-12\times \left(\frac{a}{b}\right)^{3}$$