Solve frac{32a^{-8}b^{3}c^-4}{4a^3b^5c^-2}

$$\frac { 32 a ^ { - 8 } b ^ { 3 } c ^ { - 4 } } { 4 a ^ { 3 } b ^ { 5 } c ^ { - 2 } }$$

Evaluate

$$\frac{8}{\left(bc\right)^{2}a^{11}}$$

Solution Steps

Cancel out 4b^{3} in both numerator and denominator.

$$\frac{8a^{-8}c^{-4}}{c^{-2}b^{2}a^{3}}$$

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

$$\frac{8}{b^{2}c^{2}a^{11}}$$

Differentiate w.r.t. c

$$-\frac{16}{b^{2}c^{3}a^{11}}$$