Solve a^6b^-5/a^-2b^7

$$\frac { a ^ { 6 } b ^ { - 5 } } { a ^ { - 2 } b ^ { 7 } }$$

Evaluate

$$\frac{a^{8}}{b^{12}}$$

Solution Steps

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

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

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

$$\frac{a^{8}}{b^{12}}$$

Differentiate w.r.t. a

$$\frac{8a^{7}}{b^{12}}$$