Slide 1 - Fort Bend ISD

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					Properties of Exponents
   Product Property
   Power of a Power Property
   Power of a Product Property
   Quotient Property
   Power of a Quotient Property
   Zero Property
   Negative Exponent Property
Product Property

  Expand the expressions and then re-combine so you can simplify the expression.


  Example 1:


       3  3  (3  3  3)(3  3  3  3)  37
         3     4



                     There are a total of 7 3’s.

      Example 2:

      xx 
        6 2
           ( x  x  x  x  x  x)(x  x)  x 8

                     There are a total of 8 x’s.
Product Property

  Expand the expressions and then re-combine so you can simplify the expression.


  Practice 1:

       8 8
           2         4
                         

   Practice 2:


        aa 
           6 3



    Practice 3:


         22 2 5       4
Product Property

  Expand the expressions and then re-combine so you can simplify the expression.


  Example 3:                     There are a total of 6 n’s.



 (m n )( mn )  (m  m  n  n  n  n)(m  n  n)  m3n 6
     2 4           2




                           There are a total of 3 m’s.

  Practice 4:

       ( y z )( y z ) 
           5 4         2
Product Property


  Look at the examples and practice problems we have worked.

  Do you notice a pattern (or rule)?


   In your own words write a rule for multiplying expressions with
   exponents.
Product Property


  Use the product property to simplify the following.
      Example 4:

                        3 8
      6 6  6
          3       8
                               6   11




      Example 5:

                      12  4
   b b  b
     12       4
                               b
                                16
Product Property


  Use the product property to simplify the following.
    Practice 5:

       55 5 
              4        7


    Practice 6:
        x x 
         3      5




     Practice 7:

      xy x y  
          5        3       4




                                                   To Table of Contents
Power of a Power Property

  Expand the expressions and then re-combine so you can simplify the expression.

  Example 1:


     4   4  4 
        3 2          3        3
                                       (4  4  4)  (4  4  4)  46

                                      There are a total of 6 4’s.


      Example 2:

        x   x  x  x  x 
            2 4           2       2        2      2


                   ( x  x )  ( x  x )  ( x  x)  ( x  x)  x 8
                         There are a total of 8 x’s.
Power of a Power Property

  Expand the expressions and then re-combine so you can simplify the expression.


  Practice 1:

     12  
          2 5


   Practice 2:


     w  
         5 3



    Practice 3:


        2  3 3
Power of a Power Property


  Look at the examples and practice problems we have worked.

  Do you notice a pattern (or rule)?


   In your own words write a rule for raising a power to a power.
Power of a Power Property


  Use the Power of a Power property to simplify the following.
      Example 3:


      5 
         3 4
                5  34
                            5
                             12




      Example 4:



      a 
         4 5
                a
                     45
                             a   20
Power of a Power Property


  Use the Power of a Power property to simplify the following.
    Practice 4:

         x 
            3 7
                   
    Practice 5:

       2  
              5 3



     Practice 6:

          d 
             11 4
                    

                                                   To Table of Contents
Power of a Product Property
  Expand the expressions and then re-combine so you can simplify the expression.

Example 1:

x y  x y  x y  x y  x y 
   2    4          2             2       2           2


             ( x  x  y)  ( x  x  y)  ( x  x  y)  ( x  x  y)  x y
                                                                                      8 4


                  There are a total of 8 x’s and 4 y’s.

   Example 2:

   3x y   3x y  3x y 
       2 5 2                 2       5       2   5


                     3  x  x  y  y  y  y  y   3  x  x  y  y  y  y  y 

                          There are a total of 2 3’s, 4 x’s and 10 y’s

                        3 x y  9x y
                         2       4 10            4 10
Power of a Product Property

  Expand the expressions and then re-combine so you can simplify the expression.


  Practice 1:

    ab 6 4
                 
   Practice 2:

     15 19     3
                      

    Practice 3:

       (2 x )  3 3
Power of a Product Property


  Look at the examples and practice problems we have worked.

  Do you notice a pattern (or rule)?


   In your own words write a rule for raising a product to a power.
Power of a Product Property


  Use the Power of a Product property to simplify the following.
      Example 3:

        5x   
                                 5
             3 5
                    5
                         1
                                      ( x )  515 x35  55 x15
                                         3 5




      Example 4:

      ab c    a   b    c 
                                     3       3        3
           6 11 3            1           6       11


                         13 63 113
                    a b c
                     a b c  3 18 33
Power of a Product Property


  Use the Power of a Product property to simplify the following.
    Practice 4:

        3x   5 4
                       
    Practice 5:

      a bc 
         5     6 4
                       

     Practice 6:

             7a  2
                       
Product, Power of a Power, and Power of a product Properties


  Use the properties of exponents to simplify the following.
      Example 5:

                            x   x
                                    3                     3
                               1                  2           4
     (3 x )  x  3
          2 3      4


                         13            23
                       3 x x                       4


                       3 x x
                         3          6         4

                               6 4
                    27x
                        27x       10
Product, Power of a Power, and Power of a product Properties


  Use the properties of exponents to simplify the following.
      Example 6:

 4a b  3a b    4    a    b 
                                        2             2           2
                                                                           3 a  b
      5   2        2 6              1             5           1                2       6


                              12           52   12
                          4  a  b  3 a  b                   2        6


                          4  a  b  3 a  b
                            2   10  2      2    6


                          4  3 a  a  b  b
                             2               10       2   2           6

                                     10 2 2 6
                          16  3  a  b
                          48a b    12 8
Product, Power of a Power, and Power of a product Properties


  Use the properties of exponents to simplify the following.
    Practice 7:

     5x   5x 
          5 2




       Practice 8:

         6x y 2x y  
                2      8   3 3




                                                          To Table of Contents
Quotient Property

  Expand the expressions and then re-combine so you can simplify the expression.


  Example 1:

       87 8  8  8  8  8  8  8
          
                 88888
        5
       8
                         
             8  8  8  8  8  8  8 Five of the 8’s in the numerator can cancel
           
                     
                 88888                with five of the 8’s in the denominator


           88                       There are two 8’s left


              82
              64
Quotient Property

  Expand the expressions and then re-combine so you can simplify the expression.


  Example 2:

       x6    x x x x x x
           
                   x x
         2
       x
              x x x x x x
                                            Two of the x’s in the numerator can cancel
                                             with two of the x’s in the denominator
                    x x
                     
             xx x x                  There are four x’s left


            x4
Quotient Property

 Expand the expressions and then re-combine so you can simplify the expression.

 Practice 1:

     126
        3
          
     12

 Practice 2:

        7
     a
       2
         
     a
Quotient Property
  Expand the expressions and then re-combine so you can simplify the expression.

  Example 3:

  m 4 n3 m  m  m  m  n  n  n
         
                mnn
       2
  mn                                              One of the m’s in the numerator can
            mmmmnnn
                                               cancel with one of the m’s in the
                                                 denominator and two of the ns in the
                mnn
                  
                                                  numerator can cancel with two of the
                                                  n’s in the denominator
             mmmn     There are three m’s left and one n left


              m3n
Quotient Property
  Expand the expressions and then re-combine so you can simplify the expression.


   Practice 3:

          a 5b 3
             2
                 
          ab
Quotient Property


  Look at the examples and practice problems we have worked.

  Do you notice a pattern (or rule)?


   In your own words write a rule for dividing expressions with
   exponents.
Quotient Property


  Use the quotient property to simplify the following.
      Example 4:
          12
          b      12  4
            4
               b       b 8
          b

      Example 5:

                              6  
                                 8
      1
                  6  
                                       6    6
                      8
                                            8 3    5

    6                      6 
            3                       3
Quotient Property
Use the quotient property to simplify the following.
    Practice 4:
                    1
                x  7
                  10

                   x
  Practice 5:      9
                  7
                    4
                      
                  7
  Practice 6
                  a3  a6
                      4
                          
                    a
    Practice 7:
                       11 4
                   x y
                    3 2
                        
                   x y
                                                   To Table of Contents
Power of a Quotient Property
  Expand the expressions and then re-combine so you can simplify the expression.

  Example 1:
            3
    x    x  x  x
            
     y   y  y  y
                  xxx
                
                  y y y
                      3
                 x
                 3
                 y
Power of a Quotient Property
  Expand the expressions and then re-combine so you can simplify the expression.

  Practice 1:
            4
    a
      
    5
Power of a Quotient Property


  Look at the examples and practice problems we have worked.

  Do you notice a pattern (or rule)?


   In your own words write a rule for raising a quotient to a power.
Power of a Quotient Property

  Use the power of a quotient property to simplify the following.

      Example 2:
               3        3
         6   6
            3
         x   x
  Example 3:
                            3
   a   1 a   1 3  a  1  a   a
           3                             3             3            3

              3
   5       5          5        125   125
Power of a Quotient Property

  Use the power of a quotient property to simplify the following.

      Practice 2:
               5
         8
           
         a

      Practice 3:

               6
       w
        
       z
Product, Power of a Power, and Power of a product, Quotient and
Power of a quotient Properties

  Use the properties of exponents to simplify the following.
      Example 4:


                           
                      3        3
       x    4            4          43
              x                      x     x    12

        5  5                      53  15
                           
                                3
       y    y                      y     y

    Practice 4:

                  2
     a  5

      7 
     b 
Product, Power of a Power, and Power of a product, Quotient and
Power of a quotient Properties

  Use the properties of exponents to simplify the following.
    Example 5:


                   2    x   214  x34
         4              4            4        4
 2x 
     3
          2x        3            1        3

               
         3 y      3    y  3  y
                                     14    14
 3y           4      1
                         4
                               1
                                 4


                                                    2 x4    12
                                                    4 4
                                                    3 y
                                                      16 x12
                                                          4
                                                      81 y
Product, Power of a Power, and Power of a product, Quotient and
Power of a quotient Properties
Use the properties of exponents to simplify the following.
    Example 6:

              2 a  b 5 23  a 3 b 5
          3                    3
    2a  b    5
                                        8 a b3    5

                    3 3                  
    3b  16  3b  16 3  b 16         27  b 16
                    3                          3


                   8 a b 3
                               8 a b
                                   5
                                              1  a 3  b 5 3
                                              3    5
                                        3 
                   27  b 16 16  27  b
                         3
                                                  2  27
                                                              3 2
                                                           ab
                                                         
                                                           54
Product, Power of a Power, and Power of a product, Quotient and
Power of a quotient Properties
Use the properties of exponents to simplify the following.
    Practice 5:
                  5
      2m  5

      9  
      3n 

    Practice 6:
            7
   x  1
        3

      8
    y  3x
Product, Power of a Power, and Power of a product, Quotient and
Power of a quotient Properties
Use the properties of exponents to simplify the following.
    Example 7:
                     3                               2                                             2
     2x y   x y              3  x y                                                       
                                                                                    4   5 2

              2    2x y    7
         3   2                       4       5
                           31 2
                                                                                              
     x   7y                                                                               
                                                                                                         x   y 
                                                             2                                                2             2
                                      x y      4       3                                                4             3

                                                                 2 x      y 
                                 3                                                  3          3
       2x y                         
                                                                         3
                                                                                                       
                 2       2
                                           
                                                                               2          2

                                       7                                                                    7
                                                                                                                    2


                                         8       6
             3 x y
       2 x y  2    6       6                                 23 x 6  8 y 6  6           8x y        14 12
                                                                                         
                7                                                   7   2
                                                                                              49
Product, Power of a Power, and Power of a Product, Quotient and
Power of a Quotient Properties
Use the properties of exponents to simplify the following.
    Practice 7:

                          
                               2
                       4
       5a 4b3 4ab
                3
                                   
        ab     b




                                                         To Table of Contents
Zero Exponent Property

    Example 1:
    Expand the expressions and simplify.


             x 5   xxxxx xxxxx
                                  
                                      1
             x 5
                   xxxxx xxxxx
                                  
                   Remember a number divided by itself is 1.


      Example 2:

       Use the Quotient rule to simplify the expression.


          x5
            5
               x x
                 55 0

          x
Zero Exponent Property

    Practice 1:
    Expand the expressions and simplify.

               4
            6
              4
                
            6

      Practice 2:

       Use the Quotient rule to simplify the expression.

                  4
             6
               4
                 
             6
Zero Exponent Property


  Look at the example and practice problems we have worked.

  Do you notice a pattern (or rule)?


   In your own words write a rule for raising a term to the zero
   power.
Zero Exponent Property

  Use the zero property to simplify the following.

      Example 3:    a  1
                     0




      Example 4:    5000  1     0




      Example 5:    (7 x y )  1
                         3   5 0


                             0
                    7
                     5  1
       Example 6:
                    x 
Zero Exponent Property

  Use the zero property to simplify the following.

      Practice 3:   (6)  0




      Practice 4:
                    1,000,000 0 
                                   0
                     5x y 
                          4    3
      Practice 5:
                          2 
                               
                     10 xy 
      Practice 6:
                        40ab10       0
                                           

                                                     To Table of Contents
Negative Exponent Property

    Example 1:
                                            Example 2:
   Expand the expressions and simplify.
                                          Use the Quotient rule to simplify the expression.

    x2         xx
        
                                               2
                                             x
    x 5
           xxxxx                           5
                                                  x 25  x3
                                             x
              x x
               
        
          xxxxx
           
             1
         
           xxx
           1
          3
          x
Negative Exponent Property

    Practice 1:
                                            Practice 2:
   Expand the expressions and simplify.
                                          Use the Quotient rule to simplify the expression.

    33                                        3  3

     7
                                                
    3                                         37
Negative Exponent Property


  Look at the example and practice problems we have worked.

  Do you notice a pattern (or rule)?


   In your own words write a rule for negative exponents.
Negative Exponent Property

  Use the negatvie exponent property to simplify the following.

                      1
                     5
      Example 3:   a  5
                      a
                            1     1
      Example 4:     5  3 
                          3
                           5     125
                      3 6
                               4
      Example 5:    4x y  3 6
                              x y
                       4      2
                     a      b
      Example 6:
                       2
                           4
                     b      a
Negative Exponent Property

  Use the negatvie exponent property to simplify the following.

                    2
      Practice 3:   9 

                    6
      Practice 4:   y 


                          5
      Practice 5:   6x y     3




                      3
      Practice 6:
                       4
                          
                     x
All Properties of Exponents


Use the properties of exponents to simplify the following.
      Example 7:
                                               1  1
        2 
               2
                        23 2 
                                          2  6
                                            6
           3

                                               2  64
  Example 8:

                        3  x         y                3
                                                3       3
                                     3     3                                 9
                                                            
                    3                                                    3
          3
      3x y    4                                    4
                                                                             x y 12


                                                              27 y 12
                                                                 9
  Example 9:                                                    x
       a 2b 4                                               a5
        3 6
               a 2( 3)b46              a5b2 
       a b                                                  b2
All Properties of Exponents


Use the properties of exponents to simplify the following.
    Practice 7:
          73
            5
              
          7
  Practice 8:


     4a b 
                  2
         5 3
                       


  Practice 9:

       4 x 2 y 4
              6
                  
        8 xy

                                                   To Table of Contents

				
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