Solve y^2/y^8

$$\frac { y ^ { 2 } } { y ^ { 8 } }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{y^{2}}{y^{8}}$$

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

$$y^{2-8}$$

Subtract 8 from 2.

$$y^{-6}$$

Differentiate w.r.t. y

$$-\frac{6}{y^{7}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{1}y^{2-8})$$

Do the arithmetic.

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

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}.

$$-6y^{-6-1}$$

Do the arithmetic.

$$-6y^{-7}$$