Solve 8k^4/2k

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

Evaluate

$$4k^{3}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

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

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

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

Subtract 1 from 4.

$$\frac{8^{1}k^{3}}{2^{1}}$$

Divide 8 by 2.

$$4k^{3}$$

Differentiate w.r.t. k

$$12k^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{8}{2}k^{4-1})$$

Do the arithmetic.

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

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}.

$$3\times 4k^{3-1}$$

Do the arithmetic.

$$12k^{2}$$