Solve x^4y^5/x^6y^2

$$\frac { x ^ { 4 } y ^ { 5 } } { x ^ { 6 } y ^ { 2 } }$$

Evaluate

$$\frac{y^{3}}{x^{2}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{x^{4}y^{5}}{x^{6}y^{2}}$$

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

$$x^{4-6}y^{5-2}$$

Subtract 6 from 4.

$$x^{-2}y^{5-2}$$

Subtract 2 from 5.

$$x^{-2}y^{3}$$

Differentiate w.r.t. x

$$-2\times \left(\frac{y}{x}\right)^{3}$$