Solve k^4/2k^2

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

Evaluate

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

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(k^{1}\right)^{4}\times \frac{1}{2k^{2}}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$1^{4}\left(k^{1}\right)^{4}\times \frac{1}{2}\times \frac{1}{k^{2}}$$

Use the Commutative Property of Multiplication.

$$1^{4}\times \frac{1}{2}\left(k^{1}\right)^{4}\times \frac{1}{k^{2}}$$

To raise a power to another power, multiply the exponents.

$$1^{4}\times \frac{1}{2}k^{4}k^{2\left(-1\right)}$$

Multiply 2 times -1.

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

To multiply powers of the same base, add their exponents.

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

Add the exponents 4 and -2.

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

Raise 2 to the power -1.

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

Differentiate w.r.t. k

$$k$$

Solution Steps

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

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

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$k^{1}$$

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

$$k$$