Solve 24s^6/4s^4

$$\frac { 24 s ^ { 6 } } { 4 s ^ { 4 } }$$

Evaluate

$$6s^{2}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(24s^{6}\right)^{1}\times \frac{1}{4s^{4}}$$

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

$$24^{1}\left(s^{6}\right)^{1}\times \frac{1}{4}\times \frac{1}{s^{4}}$$

Use the Commutative Property of Multiplication.

$$24^{1}\times \frac{1}{4}\left(s^{6}\right)^{1}\times \frac{1}{s^{4}}$$

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

$$24^{1}\times \frac{1}{4}s^{6}s^{4\left(-1\right)}$$

Multiply 4 times -1.

$$24^{1}\times \frac{1}{4}s^{6}s^{-4}$$

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

$$24^{1}\times \frac{1}{4}s^{6-4}$$

Add the exponents 6 and -4.

$$24^{1}\times \frac{1}{4}s^{2}$$

Raise 24 to the power 1.

$$24\times \frac{1}{4}s^{2}$$

Multiply 24 times \frac{1}{4}.

$$6s^{2}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{24^{1}s^{6}}{4^{1}s^{4}}$$

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

$$\frac{24^{1}s^{6-4}}{4^{1}}$$

Subtract 4 from 6.

$$\frac{24^{1}s^{2}}{4^{1}}$$

Divide 24 by 4.

$$6s^{2}$$

Differentiate w.r.t. s

$$12s$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}s}(\frac{24}{4}s^{6-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}s}(6s^{2})$$

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}.

$$2\times 6s^{2-1}$$

Do the arithmetic.

$$12s^{1}$$

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

$$12s$$