Solve k^7/k^2

$$\frac{ { k }^{ 7 } }{ { k }^{ 2 } }$$

Evaluate

$$k^{5}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{k^{7}}{k^{2}}$$

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

$$k^{7-2}$$

Subtract 2 from 7.

$$k^{5}$$

Differentiate w.r.t. k

$$5k^{4}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{1}{1}k^{7-2})$$

Do the arithmetic.

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

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}.

$$5k^{5-1}$$

Do the arithmetic.

$$5k^{4}$$