Question

Help please! Due in 30 minutes!

Use complete sentences to answer the following question.

1. Choose one of the properties of exponents (for example, the Power of a Power Rule). Explain how the property works, and provide an example of the property.

Answer 1

Product of a Power: When you multiply exponentials with the same base, you add their exponents (or powers). Power to a Power: When you have a power to a power, you multiply the exponents (or powers). Quotient of Powers: When you divide exponentials with the same base, you subtract the exponents (or powers).

Explanation:

Answer 2

What is the Power rule?

The Power rule tells us how to differentiate expressions of the form x^nx

n

x, start superscript, n, end superscript (in other words, expressions with xxx raised to any power):

\dfrac{d}{dx}x^n=n\cdot x^{n-1}

dx

d

x

n

=n⋅x

n−1

start fraction, d, divided by, d, x, end fraction, x, start superscript, n, end superscript, equals, n, dot, x, start superscript, n, minus, 1, end superscript

Basically, you take the power and multiply it by the expression, then you reduce the power by 111.

Example: What is the derivative of x2 ?

For x2 we use the Power Rule with n=2:

The derivative of x2 = 2x(2-1)

= 2x1

= 2x

Answer: the derivative of x2 is 2x