Solve a^3*b^-5/a^-3*b^4

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

Evaluate

$$\frac{a^{6}}{b^{9}}$$

Solution Steps

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

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

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

$$\frac{a^{6}}{b^{9}}$$

Differentiate w.r.t. a

$$\frac{6a^{5}}{b^{9}}$$