1 / 16

Hawkes Learning Systems: College Algebra

Hawkes Learning Systems: College Algebra. Section 1.3a: Properties of Exponents. Objectives. Natural number exponents. Integer exponents. Properties of exponents and their use. Natural Number Exponents. If a is any real number and if n is any natural number then

maris
Télécharger la présentation

Hawkes Learning Systems: College Algebra

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Hawkes Learning Systems: College Algebra Section 1.3a: Properties of Exponents

  2. Objectives • Natural number exponents. • Integer exponents. • Properties of exponents and their use.

  3. Natural Number Exponents If a is any real number and if n is any natural number then In the expression a is called the base and n is the exponent. Note: Read “a to the power” base exponent

  4. Example 1: Natural Number Exponents

  5. Integer Exponents If n and m are natural numbers, then Thus, . n factors m factors

  6. 0 as an Exponent If n=0, then . This suggests the following: For any real number , we define

  7. Integer Exponents Consider the following: The result is 1/2 of the result from the previous line. What, then, do you know about the following expressions with negative exponents? The exponent is decreased by one at each step.

  8. Integer Exponents Negative Integer Exponents For any real number and for any natural number n, ( simply to avoid the possibility of division by 0.)

  9. Example 2: Integer Exponents Simply the following. a. b. c. Continued on the next slide…

  10. Example 2: Integer Exponents (cont.) d. e.

  11. Properties of Exponents and Their Use Properties of Exponents Throughout this table, a and b may be taken to represent constants, variables or more complicated algebraic expressions. The letters n and m represent integers. Property 1. 2. 3. Example

  12. Properties of Exponents and Their Use Property 4. 5. 6. Example

  13. Example 3: Properties of Exponents and Their Use Simplify the following by using the properties of exponents. Write the final answer with only positive exponents. a. Any non-zero expression with an exponent of 0 is 1. Continued on the next slide…

  14. Example 3: Properties of Exponents and Their Use (cont.) b. We could have used the same properties in a different order to achieve the same result. Ex:

  15. Example 4: Properties of Exponents and Their Use Simplify the following by using the properties of exponents. Write the final answer with only positive exponents.

  16. Properties of Exponents and Their Use The first column contains example of common errors and the second column contains the corrected statements. Incorrect Statements Correct Statements

More Related