Docstoc
EXCLUSIVE OFFER FOR DOCSTOC USERS
Try the all-new QuickBooks Online for FREE.  No credit card required.

5.1 Use Properties of Exponents

Document Sample
5.1 Use Properties of Exponents Powered By Docstoc
					Warm-Up, 1
Consider the algebraic expression 3(a + 2b).
 We usually think of this as 3 distributed
 through the parenthesis, but it also means
 3 copies of a + 2b:




     a + 2b   +     a + 2b    +    a + 2b
Warm-Up, 2
Make a drawing to represent the algebraic
 expression 4(2a + 3b)
Warm-Up, 3
Make a drawing to represent the algebraic
 expression (2a + 3b)4
5.1: Use Properties of Exponents

                 Objectives:
1. To simplify numeric and algebraic
   expressions using the properties of
   exponents
Vocabulary
As a group, define      Base         Exponent
 each of these
 without your book.     Scientific
                        Notation
 Give an example of
 each word and
 leave a bit of space
 for additions and
 revisions.
Exponents
                 • Exponents mean
      Exponent     repeated
                   multiplication


     2 3     = 222
     Base
Exercise 1
1.   Write 24 in expanded form.
2.   Write x3 in expanded form.
3.   Simplify (23)2
4.   Simplify 2x2 ÷ x
Investigation 1
In this Investigation, we will
  (re)discover some
  general properties of
  exponents. They include
  the Multiplication and
                                 xy
  Division Properties, and
  Power Properties.
Investigation 1: Multiplication
Step 1: Rewrite each product in expanded
  form, and then rewrite it in exponential
  form with a single base.
   34·32     103·106      x3·x5      a2·a4
Step 2: Compare your answers to the
  original product. Is there a shortcut?
Step 3: Generalize your observations by
  filling in the blank: bm·bn = b-?-
Investigation 1: Powers
Step 1: Rewrite each expression without
  parentheses.
   (45)2      (x3)4      (5m)n      (xy)3
Step 2: Generalize your observations by
  filling in the blanks:
             (bm)n = b-?-
             (ab)n = a-?-b-?-
Investigation 1: Division
Step 1: Write the numerator and denominator in
  expanded form, and then reduce to eliminate
  common factors. Rewrite the factors that remain
  with exponents.
               9         3     3      4 6
           5            3 5         4 x
               6               2      2 3
           5            3 5         4 x
Step 2: Generalize your observations by filling in
               n
  the blank: b       ?
                 b
              m
                   b
Properties of Exponents

Multiplication      Power         Division
 Property of     Properties of   Property of
 Exponents        Exponents      Exponents


                                  n
                 (bm)n = bmn     b      nm
bm·bn = bm+n
                 (ab)n = anbn      m
                                     b
                                 b
Exercise 2
Practice simplifying expressions.


1. x2x5                   2. (2x2y)3



     m9
3.                        4. a3b7
     m6
Exercise 3
Simplify (3x + 2)2
Not the Power Property
Notice that when expanding (3x + 2)2, you
 don’t get to use the Power Property of
 exponents to “distribute” the exponent
 through the parenthesis.

The Power Property of Exponents only works
 across multiplication and division NOT
 addition or subtraction!
Exercise 4
Evaluate the expression.


1. (42)3                   2. (−8)(−8)3


                                  3
                                2
3.   (−325)3              4.    
                                9
Exercise 5
Use the division property of exponents to
 rewrite each expression with a single
 exponent. Then expand each original
 expression and simplify. Compare your
 answers.

      2          3          4          5
  3          x          7          x
      4          6          4          5
  3         x           7          x
Properties of Exponents

 Negative Exponents   Zero Exponents


       n     1
   b         n
             b
                         b0 = 1
     1
      n
         b n

    b
Exercise 6
Simplify the expression.


1. 12−4                    2. w5w−8w6


            2
    c                            2 4 5
                                20x y     z
3.  4                   4.
   d                             4
                                 4 x yz   3
Always Look on the Bright Side of Life…

When you simplify an algebraic expression
 involving exponents, all the exponents
 must be POSITIVE.
                  n
            abc         ab
                        n
              d         dc
• Negative exponents in the numerator need
  to go in the denominator
Always Look on the Bright Side of Life…

When you simplify an algebraic expression
 involving exponents, all the exponents
 must be POSITIVE.
                              n
              ab        abc
                n    
             dc          d
• Negative exponents in the denominator
  need to go in the numerator
Exercise 7
Simply the expression.


     6 5 3
1. x x x                 2.      7y 2 z 5      y 4 z 1   
                                                   3
    s 
            2
                            x y    4   2
3.  4                 4.  3 6 
   t                       x y 
Exercise 8
The radius of Jupiter
 is about 11 times
 greater than the
 radius of earth.
 How many times as
 great as Earth’s
 volume is Jupiter’s
 volume?                   4 3
                        V  r
                           3
Exercise 9
                              3 5 9
The area of a rectangle is 16a b c units2.
 Find the length of the rectangle if its width
      2  3
 is 2a bc units.
Exercise 10
Let’s say the number c x 10n is in scientific
  notation. What must be true about c?
  What must be true about n?
Scientific Notation
The number c x 10n is in scientific notation
  when 1 ≤ c < 10 and n is an integer.
• Easy to multiply, divide, and raise to
  powers using the properties of exponents
• NOT so easy to add and subtract
Exercise 11
Write the answer in scientific notation.


                                          
                                   7.5 108 4.5 104   
  
1. 4.2 103
              1.5 10 
                       6
                            2.
                                       1.5 107   
Assignment
• P. 333-335: 1, 2, 3-
  21 M3, 24-36 even,
  39-45, 47, 50, 52,
  54-56
• Further Work with
  Exponents
  Worksheet: Evens

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:29
posted:1/17/2012
language:English
pages:28