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# Section 4.7 And 4.8 Plus Warm Ups

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Multiplying Exponents, Dividing Exponents, and taking the power of a Power.

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### Section 4.7 And 4.8 Plus Warm Ups

1. 1. Warm Ups <ul><li>-7 • c • c • c • y • y = </li></ul><ul><li>Is 45 divisible by 3? </li></ul><ul><li>When solving a problem with exponents and grouping symbols, which do you do first? </li></ul><ul><li>What is a composite number? </li></ul><ul><li>What strategy do we use to find prime factors of a number? </li></ul>
2. 2. Section 4.7: Exponents and Multiplication The Exponential Jungle. October 16 th Notes Need your thinking caps today so stay with me.
3. 3. Multiplying Exponents: You Figure It Out <ul><li>7 2  7 3 = </li></ul><ul><li>5 4  5 2 = </li></ul><ul><li>b 7  b 1 = </li></ul><ul><li>Hint: Expand the exponents. </li></ul>
4. 4. Multiplying Exponents <ul><li>To multiply numbers OR variables with the same base, add the exponents. </li></ul><ul><li>Arithmetic: 2 3  2 4 = 2 3+4 = 2 7 </li></ul><ul><li>2  2  2  2  2  2  2 = 2 7 </li></ul><ul><li>Algebra: p m  p n = p m+n = p m+n </li></ul>
5. 5. So SIMPLIFY! <ul><li>3  3 3 = </li></ul><ul><li>a 5  a  b 2 = </li></ul><ul><li>x 2  x 3  y  y 4 = </li></ul><ul><li>-2x 2  3x 5 = </li></ul><ul><li>4x 2  3x 4 = </li></ul>
6. 6. Finding a Power of a Power <ul><li>(7 2 ) 3 = </li></ul><ul><li>Rule for Multiplying Powers with the Same Base. </li></ul><ul><li>Raise a power to a power by multiplying the exponents. </li></ul><ul><li>(7 2 ) 3 = (7 2 )  (7 2 )  (7 2 ) = 7 2+2+2 = 7 6 </li></ul><ul><li>OR! (7 2 ) 3 = 7 2  3 = 7 6 </li></ul><ul><li>Remember your Order of Operations. Get stuff done inside the PARENTHESES first, then the EXPONENTS! </li></ul>
7. 7. Simplify each expression. <ul><li>(2 4 ) 2 = </li></ul><ul><li>(c 5 ) 4 = </li></ul><ul><li>(m 3 ) 2 = </li></ul>
8. 8. Section 4.8: Exponents and Division The Exponential Jungle. October 16 th Notes
9. 9. Dividing Powers with the Same Base. <ul><li>7 8 /7 3 = </li></ul><ul><li>11 6 /11 5 = </li></ul>
10. 10. Dividing Powers with the Same Base. <ul><li>To divide numbers or variables with the same nonzero base , you subtract exponents. </li></ul><ul><li>Arithmetic: 4 5 /4 2 = 4 5-2 = 4 3 </li></ul><ul><li>Algebra: a m /a n = a m-n </li></ul><ul><li>Try these : </li></ul><ul><li>12m 5 /3m = </li></ul><ul><li>200m 200 /100m 100 = </li></ul>
11. 11. Simplifying Expressions with Integer Exponents <ul><li>What happens when you divide powers with the same base and get zero as the exponent? Like this…write with a fraction bar. </li></ul><ul><li>3 4 /3 4 = </li></ul><ul><li>3 4 /3 4 = 3 4-4 = 0 = 3 0 </li></ul><ul><li>ZERO AS AN EXPONENT Rule : </li></ul><ul><li>3 0 = 1 </li></ul><ul><li>a 0 = 1, when a  0 </li></ul>
12. 12. Try These: <ul><li>(-8) 2 /(-8) 2 = </li></ul><ul><li>6b 3 /18b 3 = </li></ul><ul><li>  </li></ul><ul><li>5x 0 = </li></ul><ul><li>5 2 x 6 /5x 6 = </li></ul>
13. 13. But..what about NEGATIVES and EXPONENTS!?!? <ul><li>What if you divide and you get a negative exponent? Write in expanded form with fraction bar. </li></ul><ul><li>3 2 /3 4 = </li></ul><ul><li>3 2 /3 4 = 3 2-4 = -2 = 3 -2 </li></ul><ul><li>3 2 /3 4 = 1/3 2 </li></ul>
14. 14. Negative Exponents <ul><li>Arithmetic: 3 -2 = 1/3 2 </li></ul><ul><li>Algebra: a -n = 1/a n </li></ul><ul><li>If you forget why these rules are true, always write the example in an expanded form. That will remind you why these rules are true. </li></ul>
15. 15. Need to Re-Write an Expression? <ul><li>When simplifying an expression with a negative exponent, you can write it as a fraction with a positive exponent: </li></ul><ul><li>4 -2 = 1/4 2 = 1/16 </li></ul><ul><li>You can also write an expression with a fraction so that there is no fraction bar: </li></ul><ul><li>1/x 2 = x -2 </li></ul>
16. 16. Example Problems: Simplify as much as you can… <ul><li>5 6 /5 8 = </li></ul><ul><li>4 5 /4 7 = </li></ul><ul><li>a 4 /a 6 = </li></ul><ul><li>3y 8 /9y 12 = </li></ul>
17. 17. Write without a Fraction Bar: <ul><li>x 2 y 3 /x 3 y = </li></ul><ul><li>b 3 /b 9 = </li></ul><ul><li>m 3 n 2 /m 6 n 8 = </li></ul><ul><li>dr 5 /d 5 r 3 = </li></ul>
18. 18. Assignment #25 <ul><li>Page 200: 11-27 odd. </li></ul><ul><li>Page 206: 17-39 odd. </li></ul><ul><li>START YOUR HOMEWORK NOW … </li></ul><ul><li>If there is time… </li></ul><ul><li>I highly recommend that you keep your notes open while you do your homework. That way you can look at your notes to remind yourself what to do when. </li></ul><ul><li>If all else fails, ORDER OF OPERATIONS ! </li></ul>