Solve 30a^-6b^3/5a^-12b^6

$$\frac { 30 a ^ { - 6 } b ^ { 3 } } { 5 a ^ { - 12 } b ^ { 6 } }$$

Evaluate

$$\frac{6a^{6}}{b^{3}}$$

Solution Steps

Cancel out 5b^{3} in both numerator and denominator.

$$\frac{6a^{-6}}{a^{-12}b^{3}}$$

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

$$\frac{6a^{6}}{b^{3}}$$

Differentiate w.r.t. b

$$-\frac{18a^{6}}{b^{4}}$$