Solve -4c^12d^5/20c^4d

$$\frac { - 4 c ^ { 12 } d ^ { 5 } } { 20 c ^ { 4 } d }$$

Evaluate

$$-\frac{d^{4}c^{8}}{5}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-4\right)^{1}c^{12}d^{5}}{20^{1}c^{4}d^{1}}$$

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

$$\frac{\left(-4\right)^{1}}{20^{1}}c^{12-4}d^{5-1}$$

Subtract 4 from 12.

$$\frac{\left(-4\right)^{1}}{20^{1}}c^{8}d^{5-1}$$

Subtract 1 from 5.

$$\frac{\left(-4\right)^{1}}{20^{1}}c^{8}d^{4}$$

Reduce the fraction \frac{-4}{20} to lowest terms by extracting and canceling out 4.

$$-\frac{1}{5}c^{8}d^{4}$$

Differentiate w.r.t. d

$$-\frac{4d^{3}c^{8}}{5}$$