Solve a^6*b^-9/b^6*a^7

$$\frac { a ^ { 6 } \cdot b ^ { - 9 } } { b ^ { 6 } \cdot a ^ { 7 } }$$

Evaluate

$$\frac{1}{ab^{15}}$$

Solution Steps

Cancel out a^{6} in both numerator and denominator.

$$\frac{b^{-9}}{ab^{6}}$$

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

$$\frac{1}{ab^{15}}$$

Differentiate w.r.t. b

$$-\frac{15}{ab^{16}}$$