Exponents

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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


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


#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!


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


Check the last slide to make sure your notes are complete


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

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Exponents