laws_of_exponents.pptx

Warm-up
¼ + ¼ + ¼ =
½ + ½ =
¾ - ¼ =
2 5/13 + 7/13 =
Goal/Objective: A-SSE.1 Interpret expressions that represent a quantity in terms of its context.
a. Interpret parts of an expression, such as terms, factors, and coefficients.
N-RN.1 Explain how the definition of the meaning of rational exponents follows from extending the
properties of integer exponents to those values, allowing for a notation for radicals in terms of rational
exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold,
so (51/3)3 must equal 5.
N-RN.2 Rewrite expressions involving radicals and rational exponents using the properties of
exponents.
Real Life Application
http://www.youtube.com/watch?v=VSgB1IWr6O4
Exponents are used to measure the strength of earth-
quakes. A level 1 earthquake is 1 x 101 , a level 2
earthquake is 1 x 102, a level 3 is 1 x 103, etc.
Graphic Organizer Distribution
What is the meaning of the expression ? 23
What is the value of the expression 23 ?
How do you know?
Class Discussion
Exponents
 3
5
exponential
base
exponent
3 3
means that is the exponential
form of t
Example:
he number
125 5 5
.
125

The Laws of Exponents:
#1: Exponential form: The exponent of a power indicates how
many times the base multiply itself.
n
n times
x x x x x x x x

      
3
Example: 5 5 5 5
  
10 x 10 x 10 x 10 x 10 =
4 x 4 x 4 x 4 x 4 x 4 =
50 x 50 x 50 =
38 =
The Laws of Exponents:
#2: Multiplicative Law of Exponents: If the bases are the same
And if the operations between the bases is multiplication, then the
result is the base powered by the sum of individual exponents .
m n m n
x x x 
 
3 4 3 4 7
Example: 2 2 2 2

  
   
3 4
7
Proof: 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2
        
      
X5 • x3 ( ) • ( ) =
52 • 57 = ( ) • ( ) =
The Laws of Exponents:
#3: Division Law of Exponents: If the bases are the same
And if the operations between the bases is division, then the
result is the base powered by the difference of individual
exponents .
m
m n m n
n
x
x x x
x

  
4
4 3 4 3 1
3
5
Example: 5 5 5 5 5
5

    
4
3
5 5 5 5 5
Proof: 5
5 5 5 5
  

 
 

laws_of_exponents.pptx
The Laws of Exponents:
#4: Exponential Law of Exponents: If the exponential form
is powered by another exponent, then the result is the base
powered by the product of individual exponents.
 
n
m mn
x x

 
2
3 3 2 6
Example: 4 4 4

 
       
2 2
3
6
Proof: 4 4 4 4 4 4 4 4 4 4
4 4 4 4 4 4 4
         
      
The Laws of Exponents:
#5: Product Law of Exponents: If the product of the bases
is powered by the same exponent, then the result is a multiplication
of individual factors of the product, each powered by the given
exponent.
 
n n n
xy x y
 
 
2
2 2
2 2
2
Proof: 2 3 4 9
Example: 36 6 2 3 2 3
36
    
   
The Laws of Exponents:
#6: Quotient Law of Exponents: If the quotient of the bases
is powered by the same exponent, then the result is both
numerator and denominator , each powered by the given
exponent.
n n
n
x x
y y
 

 
 
3 3
3
2 2
Example:
7 7
 

 
 
The Laws of Exponents:
#7: Negative Law of Exponents: If the base is powered by the
negative exponent, then the base becomes reciprocal with the
positive exponent.
1
m
m
x
x


3
3
1 1
Example #1: 2
2 8

 
3
3
3
1 5
Example #2: 5 125
5 1

  
The Laws of Exponents:
#8: Zero Law of Exponents: Any base powered by zero exponent
equals one
0
1
x 
 
0
0
0
Example: 112 1
5
1
7
1
flower

 

 
 

laws_of_exponents.pptx
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laws_of_exponents.pptx

  • 1. Warm-up ¼ + ¼ + ¼ = ½ + ½ = ¾ - ¼ = 2 5/13 + 7/13 =
  • 2. Goal/Objective: A-SSE.1 Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, and coefficients. N-RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5. N-RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.
  • 3. Real Life Application http://www.youtube.com/watch?v=VSgB1IWr6O4 Exponents are used to measure the strength of earth- quakes. A level 1 earthquake is 1 x 101 , a level 2 earthquake is 1 x 102, a level 3 is 1 x 103, etc.
  • 4. Graphic Organizer Distribution What is the meaning of the expression ? 23 What is the value of the expression 23 ? How do you know? Class Discussion
  • 5. Exponents  3 5 exponential base exponent 3 3 means that is the exponential form of t Example: he number 125 5 5 . 125 
  • 6. The Laws of Exponents: #1: Exponential form: The exponent of a power indicates how many times the base multiply itself. n n times x x x x x x x x         3 Example: 5 5 5 5   
  • 7. 10 x 10 x 10 x 10 x 10 = 4 x 4 x 4 x 4 x 4 x 4 = 50 x 50 x 50 = 38 =
  • 8. The Laws of Exponents: #2: Multiplicative Law of Exponents: If the bases are the same And if the operations between the bases is multiplication, then the result is the base powered by the sum of individual exponents . m n m n x x x    3 4 3 4 7 Example: 2 2 2 2         3 4 7 Proof: 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2                
  • 9. X5 • x3 ( ) • ( ) = 52 • 57 = ( ) • ( ) =
  • 10. The Laws of Exponents: #3: Division Law of Exponents: If the bases are the same And if the operations between the bases is division, then the result is the base powered by the difference of individual exponents . m m n m n n x x x x x     4 4 3 4 3 1 3 5 Example: 5 5 5 5 5 5       4 3 5 5 5 5 5 Proof: 5 5 5 5 5         
  • 12. The Laws of Exponents: #4: Exponential Law of Exponents: If the exponential form is powered by another exponent, then the result is the base powered by the product of individual exponents.   n m mn x x    2 3 3 2 6 Example: 4 4 4            2 2 3 6 Proof: 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4                 
  • 13. The Laws of Exponents: #5: Product Law of Exponents: If the product of the bases is powered by the same exponent, then the result is a multiplication of individual factors of the product, each powered by the given exponent.   n n n xy x y     2 2 2 2 2 2 Proof: 2 3 4 9 Example: 36 6 2 3 2 3 36         
  • 14. The Laws of Exponents: #6: Quotient Law of Exponents: If the quotient of the bases is powered by the same exponent, then the result is both numerator and denominator , each powered by the given exponent. n n n x x y y        3 3 3 2 2 Example: 7 7       
  • 15. The Laws of Exponents: #7: Negative Law of Exponents: If the base is powered by the negative exponent, then the base becomes reciprocal with the positive exponent. 1 m m x x   3 3 1 1 Example #1: 2 2 8    3 3 3 1 5 Example #2: 5 125 5 1    
  • 16. The Laws of Exponents: #8: Zero Law of Exponents: Any base powered by zero exponent equals one 0 1 x    0 0 0 Example: 112 1 5 1 7 1 flower         