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Section 4.7 And 4.8 Plus Warm Ups
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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.

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

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Transcript

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