Solve k^5/k^9=

$$\frac { k ^ { 5 } } { k ^ { 9 } } =$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{k^{5}}{k^{9}}$$

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

$$k^{5-9}$$

Subtract 9 from 5.

$$k^{-4}$$

Differentiate w.r.t. k

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{1}{1}k^{5-9})$$

Do the arithmetic.

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

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}.

$$-4k^{-4-1}$$

Do the arithmetic.

$$-4k^{-5}$$