Solve 5u^4v^5/20u^3v^4

$$\frac { 5 u ^ { 4 } v ^ { 5 } } { 20 u ^ { 3 } v ^ { 4 } }$$

Evaluate

$$\frac{uv}{4}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{5^{1}u^{4}v^{5}}{20^{1}u^{3}v^{4}}$$

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

$$\frac{5^{1}}{20^{1}}u^{4-3}v^{5-4}$$

Subtract 3 from 4.

$$\frac{5^{1}}{20^{1}}u^{1}v^{5-4}$$

Subtract 4 from 5.

$$\frac{5^{1}}{20^{1}}uv^{1}$$

Reduce the fraction \frac{5}{20} to lowest terms by extracting and canceling out 5.

$$\frac{1}{4}uv$$

Differentiate w.r.t. v

$$\frac{u}{4}$$