Solve y^18/y^6

$$\frac { y ^ { 18 } } { y ^ { 6 } }$$

Evaluate

$$y^{12}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{y^{18}}{y^{6}}$$

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

$$y^{18-6}$$

Subtract 6 from 18.

$$y^{12}$$

Differentiate w.r.t. y

$$12y^{11}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{1}y^{18-6})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{12})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

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

Do the arithmetic.

$$12y^{11}$$