1. EQ: How can you evaluate negative exponents?

2. Definition of an exponent
An exponent tells how many times a number is multiplied by itself. 4 3
Exponent
Base 4
= (3)(3)(3)(3) = 81 3

3. How to read an exponent
Three to the fourth power 4 3

4. How to read an exponent (cont’d)
Three to the 2nd power or
Three squared 2 3

5. How to read an exponent (cont’d)
Three to the 3rd power or
Three cubed 3 3

6. Area = (length)(width)
Exponents are often used in area problems to show the units are squared
Area = (length)(width)
Length = 30 ft
Width = 15 ft
Area = (30 ft)(15 ft) = 450 ft
15ft
30ft 2

7. A = π(8cm)2
A = 64π cm2

8. Volume = (length)(width)(height)
Exponents are often used in volume problems to show the units are cubed
Volume = (length)(width)(height)
Length = 10 cm
Width = 10 cm
Height = 20 cm
Volume = (20cm)(10cm)(10cm) = 2,000 cm 20 10 10 3

9. What is the exponent? 4
(5)(5)(5)(5) = 5

10. What is the answer? 3 5
125 =

11. What is the base and the exponent?5
(7)(7)(7)(7)(7) = 7

12. What is the base and the exponent?6
(x)(x)(x)(x)(x)(x) = x

13. What the base and the exponent?3 2
(a)(a)(a)(b)(b)(c) = a b c

14. Compute: (-4)2
Answer: (-4)(-4) = 16

15. PEMDAS
Calculate: -42
Answer: -(4)(4) = -16

16. Simplify: n2 when n = -5
Answer: (-5)2 = (-5)(-5) = 25

17. Simplify: -n2 when n = -5
Answer: -(-5)2 = -(-5)(-5) = -25

18. Compute: (-6)2
Answer: (-6)(-6) = 36

19. Compute: -62
Answer: -(6)(6) = -36

20. Compute: -(-6)2
Answer: -(-6)(-6) = -36

21. Simplify: (x + 3)2
Answer: (x + 3)(x + 3)
x2 + 6x + 9

22. Compute: 02
Answer: (0)(0) = 0

23. Compute: 20
Answer: 1
Yes, it’s 1…explanation will follow

24. WHY is anything to the power zero "1"
36 = 729
35 = 243
34 = 81
33 = 27
32 = 9
31 = 3
30 = 1

25. Laws of Exponents

26. A monomial is an algebraic expression consisting of only one term.
A term may be a number, a variable, or a product or quotient of numbers and variables (separated by a + or –)
Examples of monomials: 3, s, 3s, 3sp, 3s2p
Open Ended: Write 3 different examples of monomials

27. Determine whether each expression is a monomial. Say yes or no
Determine whether each expression is a monomial. Say yes or no. Explain your reasoning.
1.) 10
1.) Yes, this is a constant, so it is a monomial.
2.) f + 24
2.) No, this expression has addition, so it has more than one term.
3.) 3ab5
3.) Yes, this expression is a product of a coefficient and variables.
4.) j
4.) Yes, single variables are monomials.

28. Zero Exponent Property (1)
Words: Any nonzero number raised to the zero power is equal to 1.
Symbols: For any nonzero number a, a0 = 1.
Examples:
1.) 120 = 1
2.)
3.)
Open Ended: Create a problem that satisfies this property!

29. Let’s practice (-4)0 -40 (Recall PEMDAS - Exponents first!) (5x)0 5x0
Simplify each expression:
(-4)0
-40 (Recall PEMDAS - Exponents first!)
(5x)0 5x0
-(-4.9)0 (Recall PEMDAS – Exponents first!)
[(3x4y7z12)5 (–5x9y3z4)2]0
Answers:
1.) 1
2.) -1
3.) 5
4.) -1
5.) Who cares about that stuff inside the square brackets? I don't, because the zero power on the outside means that the value of the entire thing is just 1.

30. SWBAT… compute problems involving zero & negative exponents Wed, 4/6
Agenda
Review problems Zero & Negative Exponent Property (20 min)
Practice – hw#1 (15 min)
Quiz (10 min)
WARM-UP
1. (5x)0
2. 5x0 3. 4.
HW: Quiz corrections
1.) 1
2.) 5
3.) –Sophia
4.) -1/8

31. 2. 5x0 3.(Teacher)0 WARM-UP Agenda 1. (5x)0 HW: workbook p.187 and 195
Lesson on monomials and exponents w/ many examples (20 min)
Zero Exponent Property
Negative Exponent Property
Practice – hw#1 (15 min)
Quiz (10 min)
WARM-UP
1. (5x)0
2. 5x0
3.(Teacher)0
HW: workbook p.187 and 195
1.) 1
2.) 5
3.) -Sophia

32. Negative Exponent Property (2)
Words: For any nonzero number a and any integer n,
a-n is the reciprocal of an.
Also, the reciprocal of a-n = an.
Symbols: For any nonzero number a and any integer n,
Examples:
Open Ended: Create a problem that satisfies this property!
Use any number for a and n.

33. Examples

34. Examples (cont’d)