Solve 10k^5/2k^2

$$\frac { 10 k ^ { 5 } } { 2 k ^ { 2 } }$$

Evaluate

$$5k^{3}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(10k^{5}\right)^{1}\times \frac{1}{2k^{2}}$$

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

$$10^{1}\left(k^{5}\right)^{1}\times \frac{1}{2}\times \frac{1}{k^{2}}$$

Use the Commutative Property of Multiplication.

$$10^{1}\times \frac{1}{2}\left(k^{5}\right)^{1}\times \frac{1}{k^{2}}$$

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

$$10^{1}\times \frac{1}{2}k^{5}k^{2\left(-1\right)}$$

Multiply 2 times -1.

$$10^{1}\times \frac{1}{2}k^{5}k^{-2}$$

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

$$10^{1}\times \frac{1}{2}k^{5-2}$$

Add the exponents 5 and -2.

$$10^{1}\times \frac{1}{2}k^{3}$$

Raise 10 to the power 1.

$$10\times \frac{1}{2}k^{3}$$

Multiply 10 times \frac{1}{2}.

$$5k^{3}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{10^{1}k^{5}}{2^{1}k^{2}}$$

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

$$\frac{10^{1}k^{5-2}}{2^{1}}$$

Subtract 2 from 5.

$$\frac{10^{1}k^{3}}{2^{1}}$$

Divide 10 by 2.

$$5k^{3}$$

Differentiate w.r.t. k

$$15k^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{10}{2}k^{5-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}k}(5k^{3})$$

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}.

$$3\times 5k^{3-1}$$

Do the arithmetic.

$$15k^{2}$$