Solve 18x^7y^7/3x^7y^5

$$\frac { 18 x ^ { 7 } y ^ { 7 } } { 3 x ^ { 7 } y ^ { 5 } }$$

Evaluate

$$6y^{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{18^{1}x^{7}y^{7}}{3^{1}x^{7}y^{5}}$$

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

$$\frac{18^{1}}{3^{1}}x^{7-7}y^{7-5}$$

Subtract 7 from 7.

$$\frac{18^{1}}{3^{1}}x^{0}y^{7-5}$$

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

$$\frac{18^{1}}{3^{1}}y^{7-5}$$

Subtract 5 from 7.

$$\frac{18^{1}}{3^{1}}y^{2}$$

Divide 18 by 3.

$$6y^{2}$$

Differentiate w.r.t. y

$$12y$$

Steps Using Definition of a Derivative

Cancel out 3y^{5}x^{7} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(6y^{2})$$

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

$$2\times 6y^{2-1}$$

Multiply 2 times 6.

$$12y^{2-1}$$

Subtract 1 from 2.

$$12y^{1}$$

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

$$12y$$