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Understanding Exponential Notation: Lessons 1-6

Dive into exponential notation with multiplication, factors, and bases. Practice exercises with positive and negative numbers. Learn the first law of exponents and how to simplify expressions. Get ready for unit pre-test!

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Understanding Exponential Notation: Lessons 1-6

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  1. Unit 1Integers, Exponents, Scientific NotationLessons 1-6

  2. Unit 1Pre-Test Today we will take the pre-test for this unit. Pre-tests are used to see what you know before we begin. Don’t get discouraged if you don’t know all or any of the answers. This is just a way to see what you already know!

  3. Lesson 1Exponential Notation • OBJECTIVE: • Students will understand what it means to raise a number to a power and represent with repeated multiplication. • Students will explain reason for some bases requiring parentheses.

  4. Lesson 1

  5. Let’s try these together! • 5 x 5 x 5 x 5 x 5 x 5= • . • . • (-2) • 3.8

  6. Think about this… • Quick write: • Why did we use the parentheses on examples 2, 3, and 4?

  7. In cases where the base is either a fraction or a negative number, it prevents ambiguity about which portion of the expression is going to be multiplied repeatedly. • For example:

  8. Try exercises 1-10 on your own!

  9. Check your answers! • 4 • 47 times • (-11.63) • 15 times • (-5) • ( ) • (-13) • (- ) • . • n times

  10. Exercise 11-12 11. Part 1:This product will be positive, why? Part 2: This product will be negative, why? 12. Odd number of negative factors yield a _________ product. Even number of negative factors yield a _________ product.

  11. Exercises 13-14 13. If n is a postive even number, then (-55) is ______________. If n is a positive odd number, then (-72.4) is ______________. 14. Is Josie correct? Why or why not?

  12. Closing! • Why bother with exponential notation? Why don’t we just write out all the multiplication? • Suppose a colony of bacteria doubles in size every 8 hours for a few days under tight laboratory conditions. If the initial size is B, what is the size of the colony after 2 days? • Answer: In 2 days there are six- 8 hours periods, so the size will be 2 B

  13. Lesson 2Multiplication of Numbers in Exponential Form • OBJECTIVE: • Students will use exponential notation. • Students will simplify exponential expressions • Students will write equivalent expressions using first law of exponents.

  14. How do I multiply different powers of the same number x; if m and n are positive integers, what is ?

  15. Let’s try these together! 1. 2. (- ) X (- )

  16. Try exercises 1-8 on your own!

  17. Exercises 1-8

  18. Check your answers!

  19. Notes • Expressions can ONLY be simplified when the bases are the SAME. • If the bases are not the same, you can rewrite them. • For example: • What factors do 2 and 8 have in common? • Using the base 2, what exponent needs to be used to equal 8?

  20. Quick write: • Can the following example be simplified using the rule of adding exponents? • Why or why not?

  21. What if there were more terms with the same base? • Tell whether the following examples can be simplified or not. Why or why not?

  22. Can the following be simplified?Exercises 11-16

  23. Check your answers!

  24. Exercises 17-20

  25. Check your answers!

  26. Notes • We have now learned how to multiply 2 different positive integer powers of the same base. • Same base add the exponents • How do you think we divide powers with the same base? • If m, n are positive integers, what is ?

  27. Example • What is ? • Expanded form: • = • What pattern do you see?

  28. Examples

  29. Exercises 21-24Try these on your own!

  30. Check your answers!

  31. If x is a non-zero number, what is it?Simplify

  32. Can the following be simplified?

  33. Exercise 31 Hint: What is the denominator of the expression in parentheses?

  34. Exercise 32

  35. Fluency Activity • When I call a number out, tell me the square of that number. • For example: 1 x 1= 1, so 1 = 1.

  36. Closing! • Summarize the lesson. • What did you learn today? • How do you multiply exponential expressions with the same bases? • How do you divide exponential expressions with the same bases?

  37. Exit Ticket: Complete and turn in for your classwork grade! • Homework: Complete for homework • Pick expressions from # 3 • Complete # 5

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