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

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

Evaluate

$$\frac{1}{x}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Subtract 5 from 4.

$$\frac{1}{x}y^{6-6}$$

Subtract 6 from 6.

$$\frac{1}{x}y^{0}$$

For any number a except 0, a^{0}=1.

$$\frac{1}{x}$$

Differentiate w.r.t. x

$$-\frac{1}{x^{2}}$$

Steps Using Definition of a Derivative

Cancel out x^{4}y^{6} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{x})$$

The derivative of ax^{n} is nax^{n-1}.

$$-x^{-1-1}$$

Subtract 1 from -1.

$$-x^{-2}$$