Looking For a Pattern by ferda.gurcan

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									       Look for Pattern
     Look for a a Pattern in
 4-2 inInteger Exponents
  4-2 Integer Exponents




                   Warm Up
                   Problem of the Day
                   Lesson Presentation




 Course
Course 3 3
           Look for a Pattern
 4-2       in Integer Exponents

    Warm Up
    Evaluate.
     1. 103              1000
     2. 100              1
     3. 102 • 102         10,000

     4. 107
                          1000
        104
     5.  106
                          1
           106

Course 3
           Look for a Pattern
 4-2       in Integer Exponents



    Problem of the Day
    Find two different numbers for the values
    of x and y that will make xy and yx equal.
    2 and 4




Course 3
           Look for a Pattern
 4-2       in Integer Exponents




     Learn to evaluate expressions with
     negative exponents and to evaluate the
     zero exponent.




Course 3
           Look for a Pattern
 4-2       in Integer Exponents


                                                             –2
           10 2     101          100          10–1          10
     10 • 10        10           1             1           1
                                              10        10 • 10
                                          1 = 0.1 1 = 0.01
       100          10           1
                                         10       100


             ÷ 10         ÷ 10         ÷ 10          ÷ 10

  Look for a pattern in the table to extend what you
  know about exponents to include negative exponents.


Course 3
           Look for a Pattern
 4-2       in Integer Exponents
    Additional Example 1A & 1B: Using a Pattern to
             Evaluate Negative Exponents
       Evaluate the powers of 10.
       A. 10–2
                        1          Extend the pattern
            10–2   =
                     10 • 10       from the table.
                       1           Multiply. Write as a
            10–2 =        = 0.01
                      100          decimal.
       B. 10–1
                      1            Extend the pattern
            10 –1 =                from the table.
                      10

            10 –1 =   1    = 0.1   Multiply. Write as a
                      10           decimal.
Course 3
           Look for a Pattern
 4-2       in Integer Exponents
                     Check It Out: Example 1A

     Evaluate the powers of 10.
       10–8
           Extend the pattern from the table.
                                    1
           10–8   =
                    10 • 10 • 10 • 10 • 10 • 10 • 10 • 10

           Multiply.
                         1
           10–8   =
                    100,000,000
           Write as a decimal.
                  = 0.00000001
Course 3
            Look for a Pattern
 4-2        in Integer Exponents
                      Check It Out: Example 1B


       10–9
        Extend the pattern from example 1A.
                                       1
       10–9       =
                    10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10
            Multiply.
                          1
           10–9   =
                    1,000,000,000
            Write as a decimal.
                   = 0.000000001

Course 3
           Look for a Pattern
 4-2       in Integer Exponents

                 NEGATIVE EXPONENTS




     Remember!
     The reciprocal of a number is 1 divided by that
     number.

Course 3
           Look for a Pattern
 4-2       in Integer Exponents
      Additional Example 2A: Evaluating Negative
                     Exponents
       Evaluate.
       5–3
                     3   Write the reciprocal; change the
           = 1
             5           sign of the exponent.

           =
               1         Find the product of three 1 ’s.
             5•5•5                                 5
                1        Simplify.
           =
               125



Course 3
           Look for a Pattern
 4-2       in Integer Exponents
      Additional Example 2B: Evaluating Negative
                     Exponents
     Evaluate.
    (–10)–3
              1 3             Write the reciprocal; change
           = –10              the sign of the exponent.

                   1                                       1 ’s.
           =                  Find the product of three
            –10 • –10 • –10                               –10

               1
           =       = –0.001   Simplify.
             –1000


Course 3
           Look for a Pattern
 4-2       in Integer Exponents
                        Check It Out: Example 2A


       Evaluate.
       4–2
                    2       Write the reciprocal; change the
           = 1
             4              sign of the exponent.

           =
              1             Find the product of two 1 ’s.
             4•4                                    4
               1            Simplify.
           =
               16



Course 3
           Look for a Pattern
 4-2       in Integer Exponents
                        Check It Out: Example 2B


    Evaluate.
    (–7)–4
               1    4            Write the reciprocal; change
           =   –7                the sign of the exponent.

           =
                   1              Find the product of four 1 ’s.
           –7 • –7 • –7 • –7                              –7

               1
           =                      Simplify.
             2401


Course 3
           Look for a Pattern
 4-2       in Integer Exponents




Course 3
           Look for a Pattern
 4-2       in Integer Exponents
Additional Example 3: Using the Order of Operations


    Evaluate 5 – (6 – 4)–3 + (– 2)0.
    5 – (6 – 4)–3 + (–2)0

    = 5 – (2)–3 + (–2)0 Subtract inside the parentheses.

    =5– 1+1                 Evaluate the exponents.
        8

    = 57                    Add and subtract from left to
       8                    right.



Course 3
           Look for a Pattern
 4-2       in Integer Exponents
                  Check It Out: Example 3

    Evaluate 3 + (7 – 4)–2 + (–8)0.
    3 + (7 – 4)–2 + (–8)0

    = 3 + (3)–2 + (–8)0 Subtract inside the parentheses.

    =3+1 +1                 Evaluate the exponents.
       9

    =41                     Add.
      9



Course 3
           Look for a Pattern
 4-2       in Integer Exponents
                                      Lesson Quiz
    Evaluate the powers of 10.

   1. 10–3                     0.001

    2. 10–7                    0.0000001

    Evaluate.
                        1
    3.     (–6)–2
                       36
                                  3
    4. 4 •       2–3   +   10–1   5
                                      24
    5.     80   – (11 –     24)–2     25
                                         65
    6.     (4w)–2   +   w–1   for w = 4 256
Course 3

								
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