Solve 4mn^3/20m^2n^4=

$$\frac { 4 m n ^ { 3 } } { 20 m ^ { 2 } n ^ { 4 } } =$$

Evaluate

$$\frac{1}{5mn}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{4^{1}m^{1}n^{3}}{20^{1}m^{2}n^{4}}$$

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

$$\frac{4^{1}}{20^{1}}m^{1-2}n^{3-4}$$

Subtract 2 from 1.

$$\frac{4^{1}}{20^{1}}\times \frac{1}{m}n^{3-4}$$

Subtract 4 from 3.

$$\frac{4^{1}}{20^{1}}\times \frac{1}{m}\times \frac{1}{n}$$

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

$$\frac{1}{5}\times \frac{1}{m}\times \frac{1}{n}$$

Differentiate w.r.t. n

$$-\frac{1}{5mn^{2}}$$