Solve a^2b^3/a^4*ab^2

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

Evaluate

$$\frac{b^{5}}{a}$$

Solution Steps

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

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

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

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

Cancel out a in both numerator and denominator.

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

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

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

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

$$\frac{b^{5}}{a}$$

Differentiate w.r.t. b

$$\frac{5b^{4}}{a}$$