Laws on Exponents

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

 

 
 
