Solve 24a^{6}b^7div(-10a^8b^2)div(-4a^3b)

$$24 a ^ { 6 } b ^ { 7 } \div ( - 10 a ^ { 8 } b ^ { 2 } ) \div ( - 4 a ^ { 3 } b )$$

Evaluate

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

Solution Steps

Express \frac{\frac{24a^{6}b^{7}}{-10a^{8}b^{2}}}{-4a^{3}b} as a single fraction.

$$\frac{24a^{6}b^{7}}{-10a^{8}b^{2}\left(-4\right)a^{3}b}$$

Cancel out 2\times 4bb^{2}a^{6} in both numerator and denominator.

$$\frac{3b^{4}}{-5\left(-1\right)a^{2}a^{3}}$$

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

$$\frac{3b^{4}}{-5\left(-1\right)a^{5}}$$

Multiply -5 and -1 to get 5.

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

Differentiate w.r.t. b

$$\frac{12b^{3}}{5a^{5}}$$