Solve v^5w^2/v^4w^6

$$\frac { v ^ { 5 } w ^ { 2 } } { v ^ { 4 } w ^ { 6 } }$$

Evaluate

$$\frac{v}{w^{4}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{v^{5}w^{2}}{v^{4}w^{6}}$$

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

$$v^{5-4}w^{2-6}$$

Subtract 4 from 5.

$$v^{1}w^{2-6}$$

Subtract 6 from 2.

$$v^{1}w^{-4}$$

For any term t, t^{1}=t.

$$vw^{-4}$$

Differentiate w.r.t. w

$$-\frac{4v}{w^{5}}$$