Solve (frac{4a^{2}b}{a^3b^2})(5a^2b/2b^4)

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

Evaluate

$$\frac{10a}{b^{4}}$$

Solution Steps

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

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

Cancel out b in both numerator and denominator.

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

Multiply \frac{4}{ab} times \frac{5a^{2}}{2b^{3}} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 2a in both numerator and denominator.

$$\frac{2\times 5a}{bb^{3}}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

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

Multiply 2 and 5 to get 10.

$$\frac{10a}{b^{4}}$$

Differentiate w.r.t. b

$$-\frac{40a}{b^{5}}$$