Solve 21k/24k^2

$$\frac { 21 k } { 24 k ^ { 2 } }$$

Evaluate

$$\frac{7}{8k}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(21k^{1}\right)^{1}\times \frac{1}{24k^{2}}$$

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

$$21^{1}\left(k^{1}\right)^{1}\times \frac{1}{24}\times \frac{1}{k^{2}}$$

Use the Commutative Property of Multiplication.

$$21^{1}\times \frac{1}{24}\left(k^{1}\right)^{1}\times \frac{1}{k^{2}}$$

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

$$21^{1}\times \frac{1}{24}k^{1}k^{2\left(-1\right)}$$

Multiply 2 times -1.

$$21^{1}\times \frac{1}{24}k^{1}k^{-2}$$

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

$$21^{1}\times \frac{1}{24}k^{1-2}$$

Add the exponents 1 and -2.

$$21^{1}\times \frac{1}{24}\times \frac{1}{k}$$

Raise 21 to the power 1.

$$21\times \frac{1}{24}\times \frac{1}{k}$$

Multiply 21 times \frac{1}{24}.

$$\frac{7}{8}\times \frac{1}{k}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{21^{1}k^{1}}{24^{1}k^{2}}$$

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

$$\frac{21^{1}k^{1-2}}{24^{1}}$$

Subtract 2 from 1.

$$\frac{21^{1}\times \frac{1}{k}}{24^{1}}$$

Reduce the fraction \frac{21}{24} to lowest terms by extracting and canceling out 3.

$$\frac{7}{8}\times \frac{1}{k}$$

Differentiate w.r.t. k

$$-\frac{7}{8k^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{21}{24}k^{1-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{7}{8}\times \frac{1}{k})$$

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}.

$$-\frac{7}{8}k^{-1-1}$$

Do the arithmetic.

$$-\frac{7}{8}k^{-2}$$