Solve 2x^3y^7/4x^3y^3

$$\frac { 2 x ^ { 3 } y ^ { 7 } } { 4 x ^ { 3 } y ^ { 3 } }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{2^{1}x^{3}y^{7}}{4^{1}x^{3}y^{3}}$$

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

$$\frac{2^{1}}{4^{1}}x^{3-3}y^{7-3}$$

Subtract 3 from 3.

$$\frac{2^{1}}{4^{1}}x^{0}y^{7-3}$$

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

$$\frac{2^{1}}{4^{1}}y^{7-3}$$

Subtract 3 from 7.

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

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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

Differentiate w.r.t. y

$$2y^{3}$$

Steps Using Definition of a Derivative

Cancel out 2x^{3}y^{3} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y^{4}}{2})$$

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

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

Multiply 4 times \frac{1}{2}.

$$2y^{4-1}$$

Subtract 1 from 4.

$$2y^{3}$$