1 / 23

Powers and Exponents

Powers and Exponents. Multiplication = short-cut addition. When you need to add the same number to itself over and over again, multiplication is a short-cut way to write the addition problem . Instead of adding 2 + 2 + 2 + 2 + 2 = 10

Télécharger la présentation

Powers and Exponents

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. Powers and Exponents

  2. Multiplication = short-cut addition When you need to add the same number to itself over and over again, multiplication is a short-cut way to write the addition problem. Instead of adding 2 + 2 + 2 + 2 + 2 = 10 multiply 2 x 5 (and get the same answer) = 10

  3. Powers = short-cut multiplication When you need to multiply the same number by itself over and over again, powers are a short-cut way to write the multiplication problem. Instead of multiplying 2 x 2 x 2 x 2 x 2 = 32 Use the power 25 (and get the same answer) = 32

  4. A power = a number written as a base number with an exponent. baseexponent Like this: 25say 2 to the 5th power

  5. The base(big number on the bottom)= the repeatedfactor in a multiplication problem. baseexponent = power factor x factor x factor x factor x factor = product 2 x 2 x 2 x 2 x 2 = 32

  6. Theexponent(little number on the top right of base) = the number of times the base is multiplied by itself. 25 2(1st time) x 2(2nd time) x 2(3rd time) x 2(4th time) x 2(5thtime) = 32

  7. How to read powers and exponents Normally, say “base number to the exponent number (expressed as ordinal number) power” 25say2 to the 5th power Ordinal numbers: 1st, 2nd, 3rd, 4th, 5th,…

  8. squared = base2 22say 2 to the 2nd power or twosquared MOST mathematicians say two squared 22=2 x 2=4

  9. cubed = base3 23say 2 to the 3rd power or twocubed MOST mathematicians say two cubed 23=2 x 2 x 2=8

  10. Common Mistake 25 ≠(does not equal)2 x 5 25 ≠(does not equal)10 25 =2 x 2 x 2 x 2 x 2= 32

  11. Common Mistake -24 ≠(does not equal)(-2)4 Without the parenthesis, positive 2 is multiplied by itself 4 times; then the answer is negative. With the parenthesis, negative 2 is multiplied by itself 4 times; then the answer becomes positive.

  12. Common mistake -24 = (-1)x(x means times)+24 = -1 x +2 x +2 x +2 x +2= -16 Why? The 1 and the positive sign are invisible. Anything x 1=anything, so 1 x 2 x 2 x 2 x 2 = 16; and negative x positive = negative

  13. Common Mistake (-2)4=- 2 x -2 x -2 x -2= +16 Why? Multiply the numbers: 2 x 2 x 2 x 2 = 16 and then multiply the signs: 1st negative x 2nd negative = positive; that positive x 3rd negative = negative; that negative x 4th negative = positive; so answer = positive 16

  14. When the exponent is 0, and the base is any number but 0, the answer is 1. 20=1 4,6380= 1 Anynumber(except the number 0)0 = 1 00 = undefined

  15. When the exponent is 1, the answer is the same number as the base number. 21=2 4,6381= 4,638 anynumber1 = the same base “any number” 01 = 0

  16. The exponent1 is usually invisible.

  17. Theinvisibleexponent 1 21=2 4,6381= 4,638 anynumber1 = the same base “any number” 01 = 0

  18. The invisibleexponent 1 2=2 4,638= 4,638 anynumber = the same “any number” as the base 0 = 0 The exponent 1 is here. Can you see it? It’s invisible. Or. It’s understood.

  19. “Write a power as a product…” power = write the short-cut way means 25 = 2 x 2 x 2 x 2 x 2 product = write the long way = answer

  20. “Find the value of the product…” means answer 25 = 2 x 2 x 2 x 2 x 2 = 32 power = product = value of the product (and value of the power)

  21. “Write prime factorization using exponents…” 125 = product 5x5x5so 125 = power 53 = answer using exponents product 5 x 5 x 5 = power 53 Same exact answer written two different ways.

  22. Congratulations! Now you know how to write a multiplication problem as a product using factors, or as a power using exponents (this can be called exponential form). You know how to (evaluate) find the value (answer) of a power.

  23. Notes for teachers Correlates with Glencoe Mathematics (Florida Edition) texts: Mathematics: Applications and Concepts Course 1: (red book) Chapter 1 Lesson 4 Powers and Exponents Mathematics: Applications and Concepts Course 2: (blue book) Chapter 1 Lesson 2: Powers and Exponents Pre-Algebra: (green book) Chapter 4 Lesson 2: Powers and Exponents For more information on my math class see http://walsh.edublogs.org

More Related