Solve frac{30a^{9}b^-7c^6}{6a^-8c^-5}

$$\frac { 30 a ^ { 9 } b ^ { - 7 } c ^ { 6 } } { 6 a ^ { - 8 } c ^ { - 5 } }$$

Evaluate

$$\frac{5c^{11}a^{17}}{b^{7}}$$

Solution Steps

Cancel out 6 in both numerator and denominator.

$$\frac{5b^{-7}c^{6}a^{9}}{a^{-8}c^{-5}}$$

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

$$5b^{-7}c^{11}a^{17}$$

Differentiate w.r.t. b

$$-\frac{35c^{11}a^{17}}{b^{8}}$$