1. 7.3 MULTIPLICATION AND EXPONENTS:
Base: A number that is multiplied repeatedly.
Exponent: A number that shows repeated multiplication.
Property: A character or attribute that something has.

2. GOAL:

3. An exponent equation has two components:
Remember:
An exponent equation has two components:
𝑏 𝑥
Exponent
Base

4. For every number a≠0 and m, n, are integers,
Multiplying powers with same base:
PROPERTIES:
For every number a≠0 and m, n, are integers,
𝑎 𝑚 ∙ 𝑎 𝑛 = 𝑎 𝑚+𝑛
Ex:
1) 41∙ 43
= 41+3
= 44
= 256
= 𝟏 𝟑 𝟐
= 𝟏 𝟗
2) 31 ∙ 3-3
= 31+-3
= 3-2

5. YOU TRY IT:
Simplify:
124 ∙12-2
(-2)5 ∙ (-2)-2
m3 ∙ m-1 ∙ m5
9-3 ∙ 92 ∙ 9-4

6. SOLUTION:
No matter what integer it is, anything to the power of zero is 1.
124 ∙12-2
 124-2
 122
 144
2) (-2)5 ∙ (-2)-2
 (-2)5-2
 (-2)3
 -8
3) m3 ∙ m-1 ∙ m5
 m3-1+5
 m7
 m7
4) ∙ 92 ∙ 9-4
 𝟏 𝟗 𝟓 
 9-5

7. For every nonzero number a, b and integer n and m
Multiplying and Scientific notation
PROPERTIES:
For every nonzero number a, b and integer n and m
(a×10n)(b×10m) = a∙b×10n+m

8. EXAMPLE:
Simplify:
(5×104)(12×10-2 )
(3×10-5)(4×10-2 )
(1.13×10-7)(9.8×105 )(3.34×1022)

9. SOLUTION:
1) (5×104)(12×10-2 )
 (5)(12)× 104-2
 60× 102
 6.0× 103
2) (3×10-5)(4×10-2 )
 (3)(4)×
 12× 10-7
 1.2× 10-6
3) (1.13×10-7)(9.8×105 )(3.34×1022)
 (1.13)(9.8)(3.34)×
 36.99× 1020
 3.699× 1021

10. VIDEO: Get a hot chocolate and enjoy this!!!.

11. 𝑎 0 = 1 For every number a, Ex: 40 = 1 (-3)0 = 1 1000 = 1
ZERO: as an exponent
PROPERTIES:
For every number a,
𝑎 0 = 1
Ex:
40 = 1
(-3)0 = 1
1000 = 1
1,000,0000 = 1
-½ 0 =-1

12. 𝑎 −𝑛 = 1 𝑎 𝑛 Ex: 2) (-3)-2 = 𝟏 (−𝟑)𝟐 = 𝟏 𝟗 1) 4-1 = 𝟏 𝟒
PROPERTIES:
Negative numbers: as an exponents
For every nonzero
number a≠0, and integer n
𝑎 −𝑛 = 1 𝑎 𝑛
Ex:
2) (-3)-2 = 𝟏 (−𝟑)𝟐 = 𝟏 𝟗
1) 4-1 = 𝟏 𝟒

13. For every number a≠0 and m, n, are integers,
Multiplying powers with same base:
PROPERTIES:
For every number a≠0 and m, n, are integers,
𝑎 𝑚 ∙ 𝑎 𝑛 = 𝑎 𝑚+𝑛
Ex:
1) 41∙ 43 = 41+3 = 44 = 256
2) 31 ∙ 3-3 = = 3-2 = 𝟏 𝟑 𝟐 = 𝟏 𝟗

14. For every nonzero number a, b and integer n and m
Multiplying and Scientific notation
PROPERTIES:
For every nonzero number a, b and integer n and m
(a×10n)(b×10m) = a∙b×10n+m

15. Exponents and Multiplication
VIDEOS:
Exponents and Multiplication

16. CLASSWORK: Page 424:
Problems: As many as needed to master the
concept.
Page: 429: Problems: As many as needed to master the