Solve 20s^9/5s^2

$$\frac { 20 s ^ { 9 } } { 5 s ^ { 2 } }$$

Evaluate

$$4s^{7}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(20s^{9}\right)^{1}\times \frac{1}{5s^{2}}$$

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

$$20^{1}\left(s^{9}\right)^{1}\times \frac{1}{5}\times \frac{1}{s^{2}}$$

Use the Commutative Property of Multiplication.

$$20^{1}\times \frac{1}{5}\left(s^{9}\right)^{1}\times \frac{1}{s^{2}}$$

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

$$20^{1}\times \frac{1}{5}s^{9}s^{2\left(-1\right)}$$

Multiply 2 times -1.

$$20^{1}\times \frac{1}{5}s^{9}s^{-2}$$

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

$$20^{1}\times \frac{1}{5}s^{9-2}$$

Add the exponents 9 and -2.

$$20^{1}\times \frac{1}{5}s^{7}$$

Raise 20 to the power 1.

$$20\times \frac{1}{5}s^{7}$$

Multiply 20 times \frac{1}{5}.

$$4s^{7}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{20^{1}s^{9}}{5^{1}s^{2}}$$

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

$$\frac{20^{1}s^{9-2}}{5^{1}}$$

Subtract 2 from 9.

$$\frac{20^{1}s^{7}}{5^{1}}$$

Divide 20 by 5.

$$4s^{7}$$

Differentiate w.r.t. s

$$28s^{6}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}s}(\frac{20}{5}s^{9-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}s}(4s^{7})$$

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}.

$$7\times 4s^{7-1}$$

Do the arithmetic.

$$28s^{6}$$