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Powers and Exponents
Powers and Exponents
Powers and Exponents
Powers and Exponents
Powers and Exponents
Powers and Exponents
Powers and Exponents
Powers and Exponents
Powers and Exponents
Powers and Exponents
Powers and Exponents
Powers and Exponents
Powers and Exponents
Powers and Exponents
Powers and Exponents
Powers and Exponents
Powers and Exponents
Powers and Exponents
Powers and Exponents
Powers and Exponents
Powers and Exponents
Powers and Exponents
Powers and Exponents
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Powers and Exponents

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6th grade level powers and exponents; correlates with Glencoe Mathematics:Course 1-Pre-Algebra

6th grade level powers and exponents; correlates with Glencoe Mathematics:Course 1-Pre-Algebra

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  • Transcript

    • 1. Powers and Exponents
    • 2. Multiplication = short-cut addition <ul><li>When you need to add the same number to itself over and over again, </li></ul><ul><li>multiplication is a short-cut way to write the addition problem . </li></ul><ul><li>Instead of adding 2 + 2 + 2 + 2 + 2 = 10 </li></ul><ul><li>multiply 2 x 5 (and get the same answer) = 10 </li></ul>
    • 3. Powers = short-cut multiplication <ul><li>When you need to multiply the same number by itself over and over again, </li></ul><ul><li>powers are a short-cut way to write the multiplication problem . </li></ul><ul><li>Instead of multiplying 2 x 2 x 2 x 2 x 2 = 32 </li></ul><ul><li>Use the power 2 5 (and get the same answer) = 32 </li></ul>
    • 4. <ul><li>A power = </li></ul><ul><li>a number written as </li></ul><ul><li>a base number with an exponent. </li></ul><ul><li>base exponent </li></ul><ul><li>Like this: </li></ul><ul><li>2 5 say 2 to the 5th power </li></ul>
    • 5. <ul><li>The base (big number on the bottom) = </li></ul><ul><li>the repeated factor in a multiplication problem. </li></ul><ul><li>base exponent = power </li></ul><ul><li>factor x factor x factor x factor x factor = product </li></ul><ul><li>2 x 2 x 2 x 2 x 2 = 32 </li></ul>
    • 6. <ul><li>The exponent (little number on the top right of base) = the number of times the base is multiplied by itself. </li></ul><ul><li>2 5 </li></ul><ul><li>2 (1 st time) x 2 (2 nd time) x 2 (3 rd time) x 2 (4 th time) x 2 (5 th time) = 32 </li></ul>
    • 7. How to read powers and exponents <ul><li>Normally, say “ base number to the exponent number (expressed as ordinal number) power” </li></ul><ul><li>2 5 say 2 to the 5th power </li></ul><ul><li>Ordinal numbers: 1 st , 2 nd , 3 rd , 4 th , 5 th ,… </li></ul>
    • 8. squared = base 2 <ul><li>2 2 say 2 to the 2nd power or two squared </li></ul><ul><li>MOST mathematicians say two squared </li></ul><ul><li>2 2 = 2 x 2 = 4 </li></ul>
    • 9. cubed = base 3 <ul><li>2 3 say 2 to the 3rd power or two cubed </li></ul><ul><li>MOST mathematicians say two cubed </li></ul><ul><li>2 3 = 2 x 2 x 2 = 8 </li></ul>
    • 10. Common Mistake <ul><li>2 5 ≠ (does not equal) 2 x 5 </li></ul><ul><li>2 5 ≠ (does not equal) 10 </li></ul><ul><li>2 5 = 2 x 2 x 2 x 2 x 2 = 32 </li></ul>
    • 11. Common Mistake <ul><li>- 2 4 ≠ (does not equal) ( - 2 ) 4 </li></ul><ul><li>With out the parenthesis, positive 2 is multiplied by itself 4 times; then the answer is negative. </li></ul><ul><li>With the parenthesis, negative 2 is multiplied by itself 4 times; then the answer becomes positive. </li></ul>
    • 12. Common mistake <ul><li>- 2 4 = (- 1 )x (x means times) + 2 4 = </li></ul><ul><li>- 1 x + 2 x + 2 x + 2 x + 2 = - 16 </li></ul>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 <ul><li>( - 2 ) 4 = - 2 x -2 x -2 x -2 = +16 </li></ul>Why? Multiply the numbers: 2 x 2 x 2 x 2 = 16 and then multiply the signs: 1 st negative x 2 nd negative = positive; that positive x 3 rd negative = negative; that negative x 4 th negative = positive; so answer = positive 16
    • 14. When the exponent is 0 , <ul><li>and the base is any number but 0, the answer is 1 . </li></ul><ul><li>2 0 = 1 </li></ul><ul><li>4,638 0 = 1 </li></ul><ul><li>Any number (except the number 0) 0 = 1 </li></ul><ul><li>0 0 = undefined </li></ul>
    • 15. When the exponent is 1 , <ul><li>the answer is the same number as the base number . </li></ul><ul><li>2 1 = 2 </li></ul><ul><li>4,638 1 = 4,638 </li></ul><ul><li>any number 1 = the same base “any number” </li></ul><ul><li>0 1 = 0 </li></ul>
    • 16. <ul><li>The exponent 1 </li></ul><ul><li>is </li></ul><ul><li>usually </li></ul><ul><li>invisible . </li></ul>
    • 17. The invisible exponent 1 <ul><li>2 1 = 2 </li></ul><ul><li>4,638 1 = 4,638 </li></ul><ul><li>any number 1 = the same base “any number” </li></ul><ul><li>0 1 = 0 </li></ul>
    • 18. <ul><li>2 = 2 </li></ul><ul><li>4,638 = 4,638 </li></ul><ul><li>any number = the same “any number” as the base </li></ul><ul><li>0 = 0 </li></ul><ul><li>The exponent 1 is here. Can you see it? It’s invisible. Or. It’s understood. </li></ul>The invisible exponent 1
    • 19. “Write a power as a product…” <ul><li>power = write the short-cut way </li></ul><ul><li>means 2 5 = </li></ul><ul><li>2 x 2 x 2 x 2 x 2 </li></ul><ul><li>product = write the long way = answer </li></ul>
    • 20. “Find the value of the product…” <ul><li>means answer </li></ul><ul><li>2 5 = 2 x 2 x 2 x 2 x 2 = 32 </li></ul><ul><li>power = product = value of the product </li></ul><ul><li> (and value of the power) </li></ul>
    • 21. “ Write prime factorization using exponents…” <ul><li>125 = product 5 x 5 x 5 so </li></ul><ul><li>125 = power 5 3 = answer using exponents </li></ul><ul><li>product 5 x 5 x 5 = power 5 3 </li></ul><ul><li>Same exact answer written two different ways. </li></ul>
    • 22. Congratulations! <ul><li>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 ). </li></ul><ul><li>You know how to (evaluate) find the value (answer) of a power. </li></ul>
    • 23. Notes for teachers <ul><li>Correlates with Glencoe Mathematics (Florida Edition) texts: </li></ul><ul><li>Mathematics: Applications and Concepts Course 1: (red book) </li></ul><ul><li>Chapter 1 Lesson 4 Powers and Exponents </li></ul><ul><li>Mathematics: Applications and Concepts Course 2: (blue book) </li></ul><ul><li>Chapter 1 Lesson 2: Powers and Exponents </li></ul><ul><li>Pre-Algebra: (green book) </li></ul><ul><li>Chapter 4 Lesson 2: Powers and Exponents </li></ul><ul><li>For more information on my math class see http:// walsh.edublogs.org </li></ul>

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