Solve frac{4a^{-4}b^5c^9}{24b^-6c^-7}

$$\frac { 4 a ^ { - 4 } b ^ { 5 } c ^ { 9 } } { 24 b ^ { - 6 } c ^ { - 7 } }$$

Evaluate

$$\frac{b^{11}c^{16}}{6a^{4}}$$

Solution Steps

Cancel out 4 in both numerator and denominator.

$$\frac{a^{-4}b^{5}c^{9}}{6c^{-7}b^{-6}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{a^{-4}b^{11}c^{16}}{6}$$

Differentiate w.r.t. a

$$-\frac{2b^{11}c^{16}}{3a^{5}}$$