Exponents

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For Learning to Happen!

•Remove all other thoughts from your mind.•Pay close attention to this lesson.•Try all of the examples.•Ignore all other distractions.


An exponent is a little number high and An exponent is a little number high and to the right of a regular or base number.to the right of a regular or base number.

83

BaseExponent


83

BaseExponent

This exponent is read This exponent is read

8 to the 3rd power, 8 to the 3rd power,

or 8 cubed.or 8 cubed.


83

BaseExponent

An exponent tells how An exponent tells how many times a number is many times a number is multiplied by itself. multiplied by itself.


83

BaseExponent

This exponent means This exponent means

8•8•8 = 512


This exponent is read This exponent is read

six to the fourth power.six to the fourth power.

6 4Base

Exponent


This exponent is read This exponent is read three to the 2three to the 2ndnd power or power or three squared.three squared.

3 2Base

Exponent


Read These Exponents

77 to the 2nd poweror 7 squared

2


Read These Exponents

1010 to the 3rd poweror 10 cubed

3


What is the Exponent?

2 • 2 • 2 = 23



a • a • a • a = a4



(bc)(bc)(bc) = (bc)3

NOTICE that you keep the parenthesis around the variables (bc) because you

are cubing all the (bc)


Write the Verbal PhasePower Verbal Phrase Means

27 “Seven to the 2nd power” 7 7“Seven squared”

35 “Five to the 3rd power” 5 5 5 “Five cubed”

49

125


Write the Verbal PhasePower Verbal Phrase Meaning

49 “Nine to the 4th power” 9 9 9 9

52 “Two to the 5th power”2 2 2 2 2


How to Multiply Out Exponents

= 3 • 3 • 3 • 33

927

81

4


How to Multiply Out Exponents

= 2 • 2 • 2 • 2 • 22

48

16

5

32


When simplifying exponents you must watch the sign and the parenthesis!

62

= 6•6 = 36

–62

= –6•6 = -36

(-6)2

=(-6)(-6) = 36

-(6)2

= - (6)(6)1 = -36


An exponent is written in An exponent is written in exponential formexponential form when it is when it is simplified.simplified.

3322aa

33

Exponential Form


An exponent is written in An exponent is written in factor formfactor form when it is written when it is written out. out.

3322aa

33= 3•3•a•a•a

Factor Form


Factored Form Exponential Form

x • 8 • y • 8 • x 82x

2y

a • b • a • 2 2a2b

1

13 p p p r r 13p3r2



5 • x • x • x 5x3

(5x)3 (5x)(5x)(5x) = 53x3

= 125x3



8(ab)(ab) 8(ab)2

= 43x3w3y3(4xwy)3 (4xwy)(4xwy)(4xwy)

= 8a2b2

= 64x3w3y3


Evaluate the expression if x = 3 and y = 4

2 2x +y2 23 +4

“Evaluate” mean to solve!

9 + 16

25


Evaluate the expression if x = 3 and y = 4

22(x+y)22(3+4)

“Evaluate” mean to solve!

98

22(7)

2(49)


Fractions With Exponents2

1

3

1 1

3 3

1

9

41

2

1 1 1 1

2 2 2 2

1

16

24

5

4 4

5 5

16

25


Fractions With Exponents

22 3

2 23 3

49

21 5

1 15 5 1

25


Fractions With Exponents

23 7

3 37 7

949

32 6

2 2 26 6 6

8216


Take out your Study Guide (blue).


An exponent tells how many times a number is multiplied by itself.

83Base

Exponent

#1

Factored Form

3 • 3 • a • a • a

Exponential Form

32a

3

x • y • x • 2 2x

2y

1

8•8•8 = 512

22 3

2 23 3 4

9


# 2When simplifying exponents you must watch the sign and the parenthesis!

52

= 5•5 = 25

–52

= – (5)•(5) = –25

(-5)2

=(-5)(-5) = 25 –(5)2

= - (5)(5) = –251


#3

1)

2)

3)

4)

25

42

310

212

5 5 25

2 2 2 2 16

10 10 10 1000

12 12 144

To find 54 on my calculator I type in 5 4^ = 625

5 yx 4 = 625

xy

x

5 4 = 625

5 4 = 625

Circle the method that works on your calculator!


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.


Evaluate the Power“Evaluate” mean to solve!

1)

2)

3)

4)

25

42

310

212

5 5 25

2 2 2 2 16

10 10 10 1000

12 12 144


7 units3

Addition:-One-Dimensional Growth

+ =+ 4 =

Multiplication: Two-Dimensional Growth

“Three added to four”

“Three times four” or “Three groups of four”

+ + =

+4 +4 4= 12 square units3(4)=

Multiplication is Repeated Addition


Exponents: Three-Dimensional Growth

“Three to the third power”“Three to the fourth power”

3 33 33 3 3 3

327 un

43 3 3 3 3 381 un

Exponents is Repeated Multiplication


Perimeter Area Volume 5

5

5

5

P = s+s+s+sP = 4s

P=4 5P=20 units

5

5

2A =s2A =5

A =25 2units

3V =s3V =5

V =125 3units

OneDimensional

TwoDimensional

ThreeDimensional

“Five Squared” “Five Cubed”

5 5

5


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!


Exponents & PowersAn exponent or power tells how manytimes a number is multiplied by itself.

34

BaseExponent

#1

25 “Five to the 2nd power” 5 5“Five squared”

37 “Seven to the 3rd power” 7 7 7 “Seven cubed”


#2

1)

2)

3)

4)

25

42

310

212

5 5 25

2 2 2 2 16

10 10 10 1000

12 12 144

To find 54 on my calculator I type in 5 4^ = 625

5 yx 4 = 625

xy

x

5 4 = 625

5 4 = 625

Circle the method that works on your calculator!

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Exponents