Solve -5a^3b^-6/20ab^4

$$\frac { - 5 a ^ { 3 } b ^ { - 6 } } { 20 a b ^ { 4 } }$$

Evaluate

$$-\frac{a^{2}}{4b^{10}}$$

Solution Steps

Cancel out 5a in both numerator and denominator.

$$\frac{-b^{-6}a^{2}}{4b^{4}}$$

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

$$\frac{-a^{2}}{4b^{10}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{a^{2}}{-4b^{10}}$$

Differentiate w.r.t. b

$$\frac{5a^{2}}{2b^{11}}$$