Rules for Exponents

Rule #1

To multiply numbers with the same base,

add the exponents

Ex : x3 . x4 = x7

Ex: 23 x 25 = 28 = (2x2x2)(2x2x2x2x2) = 256

Rule #2

To raise a number with an exponent to a power, multiply the exponents

Ex: (x2)5 = x10

Ex: (82)3 = 86 = 8x8x8x8x8x8 = 262,144

Ex: (8x)3 = (8x)(8x)(8x) = 512x3

Rule #3

To divide two numbers with the same base, subtract the exponents

Ex: x7 = x2Ex: _75_ = 73

X5 72

Ex: x3 = x-3 =_1_ Ex: _53_ = 5-2 = _1_

X6 x3 55 52

ZERO PROPERTY OF EXPONENTS

  • Any number raised to the zero power equals 1
  • X0 = 1 50 = 1 4320 = 1

M8N1.i Review

Rule 1: Calculating with Powers

Problem / Expanded Form / How many of the base? / Exponential Notation
EX. 42 ∙ 43 / (4 ∙4)(4∙4∙4) / 5 / 45
  1. 35 ∙33

  1. 82 ∙85

  1. 102∙105

  1. x4∙x3

  1. What pattern do you notice?

Rule 2: Calculating Powers of a Power

Problem / Apply Powers Rule / Answer
EX. (42)2 / 4(2x2)=44 / 4∙4∙4∙4 = 256
6. (23)5
7. (62)3
8. (25)4
9. (-32)2
10. (43)1

Rule 3: Calculating Quotients using Exponents

Problem / Expanded Form / Simplified / How many of the base? / Exponential Notation
EX. 64
62 / 6∙6∙6∙6
6∙6 / 6∙6
1 / 2 / 62= 62
1
  1. 56
53
  1. 104
102
EX. 83
85 / 8∙8∙8___
8∙8∙8∙8∙8 / 1__
8∙8 / 2 / _1_ = 8-2
82
  1. 77
710
  1. 33
38
  1. What pattern do you notice?

Rule 4: Zero Products of Exponents

16. What happens when you divide a number by itself?

17. 36 ÷ 36 =

18. 62 ÷ 62=

19. 62 =

62

20. 6_ (What is the exponent that makes thisexpression equal 1)

21. 80=

22. 20=

23. X0=

24. Any number to the Zero Power equals ___