Solve a^-2b^-2c/a^-3c^9

$$\frac { a ^ { - 2 } b ^ { - 2 } c } { a ^ { - 3 } c ^ { 9 } }$$

Evaluate

$$\frac{a}{b^{2}c^{8}}$$

Solution Steps

Cancel out c in both numerator and denominator.

$$\frac{a^{-2}b^{-2}}{a^{-3}c^{8}}$$

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

$$\frac{b^{-2}a^{1}}{c^{8}}$$

Calculate a to the power of 1 and get a.

$$\frac{b^{-2}a}{c^{8}}$$

Differentiate w.r.t. a

$$\frac{1}{b^{2}c^{8}}$$