1. Exponents

2. For Learning to Happen! Exponents
Remove all other thoughts from your mind.
Pay close attention to this lesson.
Try all of the examples.
Ignore all other distractions.

3. Exponents
An exponent is a little number high and to the right of a regular or base number. 3 8
Exponent
Base

4. 8 This exponent is read 8 to the 3rd power, or 8 cubed. 3 Exponent
Exponents
This exponent is read
8 to the 3rd power,
or 8 cubed. 3 8
Exponent
Base

5. 8 An exponent tells how many times a number is multiplied by itself. 3
Exponents
An exponent tells how many times a number is multiplied by itself. 3 8
Exponent
Base

6. Exponents
This exponent means
8•8•8
= 512 3 8
Exponent
Base

7. 6 This exponent is read six to the fourth power. 4 Exponent Base
Exponents
This exponent is read
six to the fourth power. 6 4
Exponent
Base

8. 3 This exponent is read three to the 2nd power or three squared. 2
Exponents
This exponent is read three to the 2nd power or three squared. 3 2
Exponent
Base

9. Exponents
Read These Exponents 2 7
7 to the 2nd power
or 7 squared

10. Exponents
Read These Exponents 3 10
10 to the 3rd power
or 10 cubed

11. Exponents
What is the Exponent? 3
2 • 2 • 2 = 2

12. Exponents
What is the Exponent? 4 a
a • a • a • a =

13. (bc)(bc)(bc) = (bc) What is the Exponent? 3 Exponents
NOTICE that you keep the parenthesis around the variables (bc) because you are cubing all the (bc)

14. Write the Verbal Phase Power Verbal Phrase Means Exponents
“Seven to the 2nd power”
“Seven squared”
“Five to the 3rd power”
“Five cubed”

15. Write the Verbal Phase Power Verbal Phrase Meaning Exponents
“Nine to the 4th power”
“Two to the 5th power”

16. How to Multiply Out Exponents
= 3 • 3 • 3 • 3 4 3 9 27 81

17. How to Multiply Out Exponents
= 2 • 2 • 2 • 2 • 2 5 2 4 8 16 32

18. 62 –62 = –6•6 = -36 (-6)2 -(6)2 1 Exponents
When simplifying exponents you must watch the sign and the parenthesis! 62
= 6•6
–62
= –6•6
= 36
= -36
(-6)2
=(-6)(-6)
-(6)2
= - (6)(6)
= 36 1
= -36

19. 32a3 An exponent is written in exponential form when it is simplified.
Exponents
An exponent is written in exponential form when it is simplified.
Exponential Form
32a3

20. Exponents
An exponent is written in factor form when it is written out.
Factor Form
32a3
= 3•3•a•a•a

21. x • 8 • y • 8 • x 82x2y 2a2b1 a • b • a • 2 13 p p p r r 13p3r2
Exponents
Factored Form
Exponential Form
x • 8 • y • 8 • x
82x2y
2a2b1
a • b • a • 2
13 p p p r r
13p3r2

22. Exponents
Factored Form
Exponential Form
5 • x • x • x
5x3
(5x)(5x)(5x)
(5x)3
= 53x3
= 125x3

23. Exponents
Factored Form
Exponential Form
8(ab)(ab)
8(ab)2
= 8a2b2
(4xwy)(4xwy)(4xwy)
= 43x3w3y3
(4xwy)3
= 64x3w3y3

24. Exponents
Evaluate the expression if x = 3 and y = 4
“Evaluate” mean to solve!

25. Exponents
Evaluate the expression if x = 3 and y = 4
“Evaluate” mean to solve!

26. Fractions With Exponents

27. Fractions With Exponents

28. Fractions With Exponents

29. Exponents The End!!! Take out your Study Guide (blue).
That’s all folks

30. 8 3 8•8•8 = 512 #1 Exponent Base 32a3 2x2y1 Exponents Factored Form
An exponent tells how many times a number is
multiplied by itself. 3 8
Exponent
8•8•8
= 512
Base
Factored Form
Exponential Form
3 • 3 • a • a • a
32a3
x • y • x • 2
2x2y1

31. 52 –52 = – (5)•(5) = –25 (-5)2 –(5)2 1 # 2 Simplifying Powers
When simplifying exponents you must watch the sign and the parenthesis! 52
= 5•5
–52
= – (5)•(5)
= 25
= –25
(-5)2
=(-5)(-5)
= - (5)(5)
–(5)2
= –25
= 25 1

32. ^ 5 4 = 625 5 4 = 625 5 4 5 = 625 4 = 625 #3 Evaluate The Power1) 2) 3) 4) #3
Evaluate The Power
To find 54 on my calculator I type in 5 ^ 4
= 625 5 4
= 625 xy 5 4 5
= 625 x 4
= 625 yx
Circle the method that works on your calculator!

33. TEACHER NOTE: The lesson above was taught for Pre-Algebra & Algebra
TEACHER NOTE: The lesson above was taught for Pre-Algebra & Algebra. The following slides were used for the class of Algebra Readiness (lower level students) and slide #18-28 were taken out of the lesson above since we were just introducing Exponents.

34. Exponents
Evaluate the Power
“Evaluate” mean to solve! 1) 2) 3) 4)

35. Addition: Exponents Multiplication: -One-Dimensional Growth 3 4
“Three added to four” + = 3 4 + =
7 units
Multiplication:
Two-Dimensional Growth
“Three times four” or
“Three groups of four” + + = 4 4 4
3(4)
12 square units + + = =

36. Exponents: Exponents Three-Dimensional Growth
“Three to the third power”
“Three to the fourth power” 3 3 3

37. Exponents P = s+s+s+s P = 4s One Dimensional Two Dimensional Three
Perimeter
Volume
Area 5 5 5 5 5 5 5 5 5
P = s+s+s+s
P = 4s
“Five Squared”
“Five Cubed”
One
Dimensional
Two
Dimensional
Three
Dimensional

38. Exponents The End!!! I am going to give you a Study Guide (blue).
Please take good notes on what we just learned!
You can use these notes to help you with homework!
You can use these notes on your test!
That’s all folks

39. 3 Exponents & Powers 4 Exponent Base #1
An exponent or power tells how many
times a number is multiplied by itself. 4
Exponent 3
Base
“Five to the 2nd power”
“Five squared”
“Seven to the 3rd power”
“Seven cubed”

40. ^ 5 4 = 625 5 4 = 625 5 4 5 = 625 4 = 625 #2 Evaluate The Power1) 2) 3) 4) #2
Evaluate The Power
To find 54 on my calculator I type in 5 ^ 4
= 625 5 4
= 625 xy 5 4 5
= 625 x 4
= 625 yx
Circle the method that works on your calculator!