Solve 6b^-3a^6/30a^-5b^-2

$$\frac { 6 b ^ { - 3 } a ^ { 6 } } { 30 a ^ { - 5 } b ^ { - 2 } }$$

Evaluate

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

Solution Steps

Cancel out 6 in both numerator and denominator.

$$\frac{b^{-3}a^{6}}{5a^{-5}b^{-2}}$$

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

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

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

$$\frac{a^{11}}{5b^{1}}$$

Calculate b to the power of 1 and get b.

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

Differentiate w.r.t. a

$$\frac{11a^{10}}{5b}$$