Solve 28k^5/-4k^2=

$$\frac { 28 k ^ { 5 } } { - 4 k ^ { 2 } } =$$

Evaluate

$$-7k^{3}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(28k^{5}\right)^{1}\times \frac{1}{-4k^{2}}$$

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

$$28^{1}\left(k^{5}\right)^{1}\times \frac{1}{-4}\times \frac{1}{k^{2}}$$

Use the Commutative Property of Multiplication.

$$28^{1}\times \frac{1}{-4}\left(k^{5}\right)^{1}\times \frac{1}{k^{2}}$$

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

$$28^{1}\times \frac{1}{-4}k^{5}k^{2\left(-1\right)}$$

Multiply 2 times -1.

$$28^{1}\times \frac{1}{-4}k^{5}k^{-2}$$

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

$$28^{1}\times \frac{1}{-4}k^{5-2}$$

Add the exponents 5 and -2.

$$28^{1}\times \frac{1}{-4}k^{3}$$

Raise 28 to the power 1.

$$28\times \frac{1}{-4}k^{3}$$

Raise -4 to the power -1.

$$28\left(-\frac{1}{4}\right)k^{3}$$

Multiply 28 times -\frac{1}{4}.

$$-7k^{3}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{28^{1}k^{5}}{\left(-4\right)^{1}k^{2}}$$

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

$$\frac{28^{1}k^{5-2}}{\left(-4\right)^{1}}$$

Subtract 2 from 5.

$$\frac{28^{1}k^{3}}{\left(-4\right)^{1}}$$

Divide 28 by -4.

$$-7k^{3}$$

Differentiate w.r.t. k

$$-21k^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{28}{-4}k^{5-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}k}(-7k^{3})$$

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}.

$$3\left(-7\right)k^{3-1}$$

Do the arithmetic.

$$-21k^{2}$$