Solve 8k^3/4k

$$\frac { 8 k ^ { 3 } } { 4 k }$$

Evaluate

$$2k^{2}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{8^{1}k^{3}}{4^{1}k^{1}}$$

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

$$\frac{8^{1}k^{3-1}}{4^{1}}$$

Subtract 1 from 3.

$$\frac{8^{1}k^{2}}{4^{1}}$$

Divide 8 by 4.

$$2k^{2}$$

Differentiate w.r.t. k

$$4k$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{8}{4}k^{3-1})$$

Do the arithmetic.

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

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}.

$$2\times 2k^{2-1}$$

Do the arithmetic.

$$4k^{1}$$

For any term t, t^{1}=t.

$$4k$$