Solve y^4/y^8

$$\frac { y ^ { 4 } } { y ^ { 8 } }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{y^{4}}{y^{8}}$$

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

$$y^{4-8}$$

Subtract 8 from 4.

$$y^{-4}$$

Differentiate w.r.t. y

$$-\frac{4}{y^{5}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{1}y^{4-8})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$-4y^{-5}$$