Solve 3/5a^3bdiv-4/5a^2b=

$$\frac { 3 } { 5 } a ^ { 3 } b \div - \frac { 4 } { 5 } a ^ { 2 } b =$$

Evaluate

$$-\frac{3b^{2}a^{5}}{4}$$

Solution Steps

Divide \frac{3}{5}a^{3}b by -\frac{4}{5} by multiplying \frac{3}{5}a^{3}b by the reciprocal of -\frac{4}{5}.

$$\frac{\frac{3}{5}a^{3}b\times 5}{-4}a^{2}b$$

Multiply \frac{3}{5} and 5 to get 3.

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

Express \frac{3a^{3}b}{-4}a^{2} as a single fraction.

$$\frac{3a^{3}ba^{2}}{-4}b$$

Express \frac{3a^{3}ba^{2}}{-4}b as a single fraction.

$$\frac{3a^{3}ba^{2}b}{-4}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{3a^{5}bb}{-4}$$

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

$$\frac{3a^{5}b^{2}}{-4}$$

Differentiate w.r.t. a

$$-\frac{15b^{2}a^{4}}{4}$$