Solve 18s^8/3s^4

$$\frac { 18 s ^ { 8 } } { 3 s ^ { 4 } }$$

Evaluate

$$6s^{4}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(18s^{8}\right)^{1}\times \frac{1}{3s^{4}}$$

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

$$18^{1}\left(s^{8}\right)^{1}\times \frac{1}{3}\times \frac{1}{s^{4}}$$

Use the Commutative Property of Multiplication.

$$18^{1}\times \frac{1}{3}\left(s^{8}\right)^{1}\times \frac{1}{s^{4}}$$

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

$$18^{1}\times \frac{1}{3}s^{8}s^{4\left(-1\right)}$$

Multiply 4 times -1.

$$18^{1}\times \frac{1}{3}s^{8}s^{-4}$$

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

$$18^{1}\times \frac{1}{3}s^{8-4}$$

Add the exponents 8 and -4.

$$18^{1}\times \frac{1}{3}s^{4}$$

Raise 18 to the power 1.

$$18\times \frac{1}{3}s^{4}$$

Multiply 18 times \frac{1}{3}.

$$6s^{4}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{18^{1}s^{8}}{3^{1}s^{4}}$$

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

$$\frac{18^{1}s^{8-4}}{3^{1}}$$

Subtract 4 from 8.

$$\frac{18^{1}s^{4}}{3^{1}}$$

Divide 18 by 3.

$$6s^{4}$$

Differentiate w.r.t. s

$$24s^{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}s}(\frac{18}{3}s^{8-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}s}(6s^{4})$$

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}.

$$4\times 6s^{4-1}$$

Do the arithmetic.

$$24s^{3}$$