1. Powers and Exponent Laws
Chapter 2
Powers and Exponent Laws

2. 2.1 – What is a power? 2.2 – Powers of ten and the Zero exponent
Chapter 2

3. Khan Academy on Exponents

4. What is a power?
Squares
Cubes
A = L2
A = 52 = 25
V = L3
V = 53 = 125

5. 53 powers Power: The expression of the base and the exponent.
Exponent: The number of times that the base will be multiplied by itself.
Base: The number that is being repeatedly multiplied by itself.

6. powers Examples: 53 = 5 x 5 x 5 35 = 3 x 3 x 3 x 3 x 3
What about negatives? How will they work?
Are (–3)4 and –34 the same?
(–3)4 = (–3) x (–3) x (–3) x (–3) = 81
–34 = –(3 x 3 x 3 x 3) = –81

7. challenge
Use these five numbers to make an expression that represents the largest possible number. You can use any operation you like (addition, subtraction, multiplication, division, exponents), but you can only use each number once.

8. Powers of ten and the zero exponent
What’s easier to write, or 1020?
Number in Words
Standard Form
Power
one million
106
one hundred thousand
105
ten thousand
10 000
104
one thousand
1 000
103
one hundred
100
102
ten 10
101
one 1

9. Zero exponent
Power
Number 44
256 43 64 42 16 41 4 40 1
You can try this with other bases, but the result will always be the same.
The Zero Exponent Law: Any base to the power of zero will be equal to one.

10. example 3045 = 3000 + 40 + 5 = (3 x 1000) + (4 x 10) + (5 x 1)
Write 3045 using powers of ten.
3045 =
= (3 x 1000) + (4 x 10) + (5 x 1)
= (3 x 103) + (4 x 101) + (5 x 100)

11. Khan video 2
Khan Video 2

12. PG # 4, 5, 7-9 (Ace), 13, 17, 21, 22, 23 PG # 4, 6, 9, 13, 14
Independent Practice

13. 2.3 – Order of operations with powers 2.4 – Exponent laws I
Chapter 2

14. B E D M A S Order of operations Brackets Exponents Division
What’s the acronym used to remember the order of operations?
B E D M A S
Brackets
Exponents
Division
Multiplication
Addition
Subtraction

15. example 33 + 23 = 27 + 8 = 35 Calculate each expression:
(3 + 2)3 =
= 35
Exponents come before Addition in BEDMAS, so we do them first.
(3 + 2)3 = 53
= 125
Brackets come before Exponents in BEDMAS, so we do them first.

16. Exponent rules Exponent Laws: am x an = am+n
Try to solve by expanding into repeated multiplication form:
73 x 74 =
(7 x 7 x 7) x (7 x 7 x 7 x 7)
= 7 x 7 x 7 x 7 x 7 x 7 x 7
= 77
What happens? What kind of rule can we make about the multiplication of powers with like bases?
Exponent Laws:
am x an = am+n

17. What’s the general rule we can make for exponent division?
Exponent rules
What about division? Try solving this one to make a general rule:
What’s the general rule we can make for exponent division?
Exponent Laws:

18. example Write each expression as a power. a) 65 x 64 b) (–9)10 ÷ (–9)6
= (–9)4
65 x 64 = 65+4
= 69
Evaluate:
32 x 34 ÷ 33
32 x 34 ÷ 33 =
= 33
= 27

19. example Evaluate. a) 62 + 63 x 62 b) (–10)4[(–10)6 ÷ (–10)4] – 107
Remember, BEDMAS, so we do multiplication first before addition.
x 62 = = =
= 7812
b) Remember, BEDMAS, so we do inside the
brackets, then multiplication, then subtraction.
(–10)4[(–10)6 ÷ (–10)4] – 107 = (–10)4[(–10)2] – 107
= (–10)4+2 – 107
= (–10)6 – 107
= –
= –

20. Pg , # 7, 10, 12, 13, 16, 20, 24, 26 pg , # 4ace, 5ace, 8, 12, 13, 15, 20
Independent Practice

21. 2.5 – Exponent laws II
Chapter 2

22. Handout: try to fill in the chart

23. A power to a power (33)5 = 33 x 33 x 33 x 33 x 33 = 315 Exponent Laws:
From what we’ve learned from the chart, what can we say about the following expression:
(33)5 =
33 x 33 x 33 x 33 x 33 =
315
Exponent Laws:

24. Exponent laws (4 x 3)6 = (4 x 3)(4 x 3)(4 x 3)(4 x 3)(4 x 3)(4 x 3)
What about something like this? Try it!
(4 x 3)6
= (4 x 3)(4 x 3)(4 x 3)(4 x 3)(4 x 3)(4 x 3)
= (4 x 4 x 4 x 4 x 4 x 4)(3 x 3 x 3 x 3 x 3 x 3)
= 46 x 36
What’s the basic rule that we can say about the what happens when we take a product or quotient to a power?

25. Exponent Laws:

26. example –(24)3 = –24x3 = –212 = –4096 Evaluate:
a) –(24)3 b) (3 x 2)2 c) (78 ÷ 13)3
–(24)3 = –24x3
= –212
= –4096
b) (3 x 2)2 = 32 x 22
= 9 x 4
= 36
c) (78 ÷ 13)3 = (6)3
= 216
Simplify, then evaluate:
(6 x 7)2 + (38 ÷ 36)3
(6 x 7)2 + (38 ÷ 36)3 = (42)2 + (32)3 = =
= 2493

27. Pg , # 8, 11, 13, 14, 16, 19, 20
Independent Practice