Solve frac{(4a^{3}b^{4})*(10a^2b^5)}{5a^4b^2}

$$\frac { ( 4 a ^ { 3 } b ^ { 4 } ) \times ( 10 a ^ { 2 } b ^ { 5 } ) } { 5 a ^ { 4 } b ^ { 2 } }$$

Evaluate

$$8ab^{7}$$

Solution Steps

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

$$\frac{4a^{5}b^{4}\times 10b^{5}}{5a^{4}b^{2}}$$

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$\frac{4a^{5}b^{9}\times 10}{5a^{4}b^{2}}$$

Cancel out 5b^{2}a^{4} in both numerator and denominator.

$$2\times 4ab^{7}$$

Multiply 2 and 4 to get 8.

$$8ab^{7}$$

Differentiate w.r.t. b

$$56ab^{6}$$