Solve 4xy^2/16xy

$$\frac { 4 x y ^ { 2 } } { 16 x y }$$

Evaluate

$$\frac{y}{4}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{4^{1}x^{1}y^{2}}{16^{1}x^{1}y^{1}}$$

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

$$\frac{4^{1}}{16^{1}}x^{1-1}y^{2-1}$$

Subtract 1 from 1.

$$\frac{4^{1}}{16^{1}}x^{0}y^{2-1}$$

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

$$\frac{4^{1}}{16^{1}}y^{2-1}$$

Subtract 1 from 2.

$$\frac{4^{1}}{16^{1}}y^{1}$$

Reduce the fraction \frac{4}{16} to lowest terms by extracting and canceling out 4.

$$\frac{1}{4}y$$

Differentiate w.r.t. y

$$\frac{1}{4} = 0.25$$

Steps Using Definition of a Derivative

Cancel out 4xy in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y}{4})$$

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

$$\frac{1}{4}y^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{4}y^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{1}{4}\times 1$$

For any term t, t\times 1=t and 1t=t.

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