Solve a^-6*b^-5*a/a^3*b^-9

$$\frac { a ^ { - 6 } \cdot b ^ { - 5 } \cdot a } { a ^ { 3 } \cdot b ^ { - 9 } }$$

Evaluate

$$\frac{b^{4}}{a^{8}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -6 and 1 to get -5.

$$\frac{a^{-5}b^{-5}}{a^{3}b^{-9}}$$

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

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

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

$$\frac{b^{4}}{a^{8}}$$

Differentiate w.r.t. b

$$\frac{4b^{3}}{a^{8}}$$