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Exponents

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Bob Morris

This document explains exponents and how secrets can spread exponentially through social networks. It provides examples of writing exponents in factored, standard, and exponential forms. Exponents represent repeated multiplication of a base number. For example, 24 means 2 x 2 x 2 x 2, or 2 raised to the fourth power. The document shows that if one person tells 3 friends a secret, and each of those 3 friends tells 3 more people, the number of people who know the secret increases exponentially from 3 to 9 after one round of sharing.

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Exponents Chapter 2 Lesson 2.8
How does a secret spread so fast? The person with a secret tells a friend. The friend promises never to tell anyone. That same friend breaks the promise and tells two more friends. The two new friends tell two new friends. The two new friends decide to tell two more friends. This pattern occurs over and over until many people have been told. By the end of the day it is no longer a secret!
Here is how a secret can spread. (Real Fast!) Round 1 Round 2 I have a secret and I tell 3 of my best friends. My 3 friends each tell 3 more people. Look how many people now know the secret! 3 x 3 = 9 9 people know!
In an exponential expression, the base is the factor, and the exponent tells the amount of times to multiple that number by itself. (That is a mouthful!) 3 4 Your BASE = 3 Your EXPONENT = 4 A base is a number that can be expressed using an exponent. An exponent is the small number and is referred to as a ¡°power.¡± 3 4 means 3 x 3 x 3 x 3 OR 3 to the forth power.
There are 3 ways to write an exponent. 2 4 Factored Form is one way. In factored form you spread the equation apart ¨C piece by piece to show what it means. 2 4 Means 2 x 2 x 2 x 2 This is factored form!
Here is another way! Write a set of numbers as an exponent x 2 x 2 x 2 = List the base first = 2 Then count up the number of two¡¯s you see. There are 4 number 2¡¯s. Therefore 2 x 2 x 2 x 2 = 2 4
Here is the last way! (The Most Important Way) Standard Form is the easiest to write. To write an exponent in standard form ¨C JUST MULTIPLY! 2 4 = 2 x 2 x 2 x 2 Now solve! 2 x 2 = 4 x 2 = 8 x 2 = 16
Try This! 3 5 ¨C Write in factored form. 4 x 4 x 4 Write as an exponent. 2 6 ¨C Write in standard form. 3 x 3 x 3 x 3 x 3 4 3 2 x 2 x 2 x 2 x 2 x 2 = 64
Exponents in Shape Form Write the factored shape in exponent form. X X =
Answer: 3
Try this! X X X X = The yellow block = y Write this factored equation as an exponent. Answer: y 5
Task Rotation Exercise I will give each student an index card with one problem. The problem will ask for you to solve the problem in standard form, factored form, and exponent form. After you complete the problem do not move until I blow the whistle. The person who has the card that says ¡°Water¡± is to complete the problem first then may leave the room to get a drink of water. When the person who gets the drink returns, I will blow the whistle and you will rotate to the next desk.
Task Rotation Answers Question Write as an exponent 4x4x4x4x4 Write as an exponent 12x12 Write as an exponent 7x7x7x7x7x7 Answers 4 5 12 2 7 6
Write in Factored Form Question 6 3 43 2 0.3 5 10 5 15 4 100 6 Answer 6x6x6 43x43 0.3 x 0.3 x 0.3 x 0.3 x 0.3 10 x 10 x 10 x 10 x 10 15 x 15 x 15 x 15 100 x 100 x 100 x 100 x 100 x 100
Write in Standard Form Questions 10 4 = 5 4 = 6 3 = 6 4 = 6 5 = Answers 10,000 625 216 1296 7776
Write as an exponent Question 15. 6x6x6x6x6 16. 74 x 74 x 74 17. 0.4 x 0.4 x 0.4 x 0.4 Answers 6 5 74 3 0.4 4
Write in Standard Form Question 2 6 = 7 4 = 4 5 = Answer 64 2401 1024
Let¡¯s Review! 5 2 Which number is the ¡°exponent?¡± Which number is the ¡°base?¡± Write the exponent in factored form? Write the exponent in standard form? 2 5 5 x 5 25
What to expect next¡­¡­ Solve 2 3 + 3 3 = Answer: 2x2x2=8 / 3x3x3=27 8 + 27 = 35
Homework Complete ¡°Reteaching 2.8¡±

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Exponents

  • 1. Exponents Chapter 2 Lesson 2.8
  • 2. How does a secret spread so fast? The person with a secret tells a friend. The friend promises never to tell anyone. That same friend breaks the promise and tells two more friends. The two new friends tell two new friends. The two new friends decide to tell two more friends. This pattern occurs over and over until many people have been told. By the end of the day it is no longer a secret!
  • 3. Here is how a secret can spread. (Real Fast!) Round 1 Round 2 I have a secret and I tell 3 of my best friends. My 3 friends each tell 3 more people. Look how many people now know the secret! 3 x 3 = 9 9 people know!
  • 4. In an exponential expression, the base is the factor, and the exponent tells the amount of times to multiple that number by itself. (That is a mouthful!) 3 4 Your BASE = 3 Your EXPONENT = 4 A base is a number that can be expressed using an exponent. An exponent is the small number and is referred to as a ¡°power.¡± 3 4 means 3 x 3 x 3 x 3 OR 3 to the forth power.
  • 5. There are 3 ways to write an exponent. 2 4 Factored Form is one way. In factored form you spread the equation apart ¨C piece by piece to show what it means. 2 4 Means 2 x 2 x 2 x 2 This is factored form!
  • 6. Here is another way! Write a set of numbers as an exponent x 2 x 2 x 2 = List the base first = 2 Then count up the number of two¡¯s you see. There are 4 number 2¡¯s. Therefore 2 x 2 x 2 x 2 = 2 4
  • 7. Here is the last way! (The Most Important Way) Standard Form is the easiest to write. To write an exponent in standard form ¨C JUST MULTIPLY! 2 4 = 2 x 2 x 2 x 2 Now solve! 2 x 2 = 4 x 2 = 8 x 2 = 16
  • 8. Try This! 3 5 ¨C Write in factored form. 4 x 4 x 4 Write as an exponent. 2 6 ¨C Write in standard form. 3 x 3 x 3 x 3 x 3 4 3 2 x 2 x 2 x 2 x 2 x 2 = 64
  • 9. Exponents in Shape Form Write the factored shape in exponent form. X X =
  • 11. Try this! X X X X = The yellow block = y Write this factored equation as an exponent. Answer: y 5
  • 12. Task Rotation Exercise I will give each student an index card with one problem. The problem will ask for you to solve the problem in standard form, factored form, and exponent form. After you complete the problem do not move until I blow the whistle. The person who has the card that says ¡°Water¡± is to complete the problem first then may leave the room to get a drink of water. When the person who gets the drink returns, I will blow the whistle and you will rotate to the next desk.
  • 13. Task Rotation Answers Question Write as an exponent 4x4x4x4x4 Write as an exponent 12x12 Write as an exponent 7x7x7x7x7x7 Answers 4 5 12 2 7 6
  • 14. Write in Factored Form Question 6 3 43 2 0.3 5 10 5 15 4 100 6 Answer 6x6x6 43x43 0.3 x 0.3 x 0.3 x 0.3 x 0.3 10 x 10 x 10 x 10 x 10 15 x 15 x 15 x 15 100 x 100 x 100 x 100 x 100 x 100
  • 15. Write in Standard Form Questions 10 4 = 5 4 = 6 3 = 6 4 = 6 5 = Answers 10,000 625 216 1296 7776
  • 16. Write as an exponent Question 15. 6x6x6x6x6 16. 74 x 74 x 74 17. 0.4 x 0.4 x 0.4 x 0.4 Answers 6 5 74 3 0.4 4
  • 17. Write in Standard Form Question 2 6 = 7 4 = 4 5 = Answer 64 2401 1024
  • 18. Let¡¯s Review! 5 2 Which number is the ¡°exponent?¡± Which number is the ¡°base?¡± Write the exponent in factored form? Write the exponent in standard form? 2 5 5 x 5 25
  • 19. What to expect next¡­¡­ Solve 2 3 + 3 3 = Answer: 2x2x2=8 / 3x3x3=27 8 + 27 = 35