Exponent Rules ppt.pptx

1. Integer
Exponents
Day 1

2. Definitions
Base: The term/variable of which is being
raised upon
Exponent: The term/variable is raised by a
term. AKA Power
m
a BASE
EXPONENT

3. m
a 3
2
2 2 2
  
2 3
 
2 2 2
  

4. Example 1
3 3 9
 
9
2
(3)

5. 5
Example 2
3 3 9
  
9
2
( 3)


6. 6
Example 3
 9
2
3


7. Solve:

8. Laws of Exponents
https://www.youtube.com/watch?v=
QIZTruxt2rQ

9. Any number raised to the first
power is …
31
=
871
=
5289211
=
Rule:
Any number raised to the first power
is
itself.
(a1
= a)

10. Any number raised to the power
of zero is ONE!
30
=
870
=
5289210
=
Rule:
a0
= 1

11. Negative Power Property
Saying goes: NO NEGATIVE POWERS
What are the base(s) and the power(s)?
 
 3
a

12. Negative Power Property
( )

1
n
n
a
a
( )
a
a


3
3
1
3
( )
a 


13. Negative Power Property
( )

1
n
n
a
a
n n
a b
b a

   
   
   


14. Practice
1) (-4)2
2) 73
3) -54
4) 101
5) 95
6) (-2)0
7) (-2)-1
8) 0-3
9) 3-4
10) (¼)0

15. Product Rule
Saying goes: BASE, BASE, ADD
If the BASES are same, ADD the powers
What are the base(s) and the power(s)?
4 5
2 2


 
m n m n
a a a

16. Product of a Power
m n m n
a a a 
 
4 5 4 5
2 2 2 
 
9
2

512
4 5
2 2
 

17. Product of a Power
m n m n
a a a 
 
4 5 4 5
2 2 2 
  
9
2

512
4 5
2 2
  

18. 4 5
2 2


2

19. Quotient Power Property
Saying goes: When dividing an expression with a
power, SUBTRACT the powers. They must have the
same base in order to subtract.
What are the base(s) and the power(s)?
8
3
x
x


m
m n
n
a
a
a

20. Quotient Power Property


m
m n
n
a
a
a


8
8 3
3
x
x
x
8
3
x
x
  5
x

21. Quotient Power Property


m
m n
n
a
a
a
3
8
x
x

 5
1
x

22. =

23. Power of a Power
 Saying goes: POWER, POWER, MULTIPLY
If the POWERS are near each other, MULTIPLY the powers
– usually deals with PARENTHESES
What are the base(s) and the power(s)?
 
3
2
3
( ) 

m n m n
a a

24. Power of a Power
( ) 

m n m n
a a
 
3
2 6
3 3

6
3

729
 
3
2
3 

25. Power of a Power
( ) 

m n m n
a a
 
2
3
2 
64

26. ( )

3 2
2

1
64

27. Power of a Product
Saying goes: DISTRIBUTE THE POWER TO THE
BASES
What are the base(s) and the power(s)?
( )4
3x
( ) 
m m m
ab a b

28. Power of a Product
( ) 
m m m
ab a b
4 4 4
(3 ) (3) ( )
x x
 
4
81 x
 
x
 4
81
4
(3 )
x 
How many
bases does this
problem have?

29. Properties of Exponents
Negative Power Property:
Product of a Power:
Power of a Power:
Quotient Power Property:
m n m n
a a a 
 
( ) 

m n m n
a a
( )

1
n
n
a
a


m
m n
n
a
a
a

30. Do Now – December 6th
NO CALCULATOR
1. Solve: 0.2x = 7 - 0.8x
2. 6-3
3. -40
4. (-8)2
5. -34