What about a

number raised to the power of ZERO?

Example: What is 30 ?

Complete the table below. See if YOU and your

partner can see the pattern to figure it out….

34 3x3x3x3 = 81

33

32

31

30

Something about Exponents

𝒙𝟑 =𝒙 ∙ 𝒙 ∙ 𝒙

𝒙𝟐 =𝒙 ∙ 𝒙

𝒙𝟏 = x

𝒙𝟎 = 1

Simplifying Exponential Expressions

An exponential expression is completely simplified if…

There are no negative exponents. (x–2)

The same base does not appear more than

once in a product or quotient. (x3y4x2)

No powers are raised to powers. (4x)5

Simplifying Exponential Expressions

No products are raised to powers.

No quotients are raised to powers.

Numerical coefficients in a quotient do

not have any common factor other

than 1.

4

)( 3z4

3

m

2

10 3x

Vocabulary

An exponent tells how many times a number

(called the base) is multiplied by itself.

baseexponent

32

32 means 3 is multiplied by itself 2 times

base

exponent

Reading Exponents

46 is read “4 to the sixth power.”

51 is read “5 to the first power.”

38 is read “3 to the eighth power.”

And so on…

There are two specially-named powers:

32 is read “3 to the second power” or “3 squared.”

43 is read “4 to the third power” or “4 cubed.”

What about a number

raised to the power of ZERO?

Example: What is 30 ?

Did you find that dividing by 3 gives you the

next value?

34 3x3x3x3= 81

33 3x3x3 =27

32 3x3 =9

31 3

30 1

What about a number

raised to the power of ZERO?

Scientific Notation Example: What is 1 x 100 ?

Take notice of the quantity of zero’s following

the 1 in each solution.

1 x 104 10,000

1 x 103 1,000

1 x 102 100

1 x 101 10

1 x 100 1

What about a number

raised to the power of ZERO?

FACT: All non-zero numbers raised to the power

of zero are equal to 1.

1. 20 = 1

2. 40 = 1

3. 1,000,0000 = 1

4. -20 = 1

Multiplication

Properties of Exponents Continued…*A power raised to another power equals that base

raised to the product of the exponents.

*

Examples:

1)

2)

3)

mnm aan

22229)3(3 xxx

2222933 xxx

5126484242 333

Multiplication

Properties of Exponents Continued…*A power raised to another power equals that base

raised to the product of the exponents.

*

Examples:

1) (𝒙𝟑)𝟒 =

2) 𝟐(𝒙𝟑)𝟑 +(𝟐𝒙𝟑)𝟑

mnm aan

Simplify the equation: you do not have to solve.

−𝟑 𝒙 𝟐 + 𝟐𝒙 𝟐 = 49

Negative Exponents

Properties of Exponents Continued…Negative exponents in the numerator get moved to the

denominator and become positive exponents.

Negative exponents in the denominator get moved to the numerator and become positive exponents.

𝒙−𝒎 =𝟏

𝒙𝒎𝟏

𝒙−𝒎= 𝒙𝒎

Multiplication

Properties of Exponents Continued…1.) 2.)

𝒙−𝟐 =𝟏

𝒙−𝟒=

3.) Solve for x.

𝟏

𝒙−𝟑= 𝟖

Simplify the equation: you do not have to solve.

−𝟑 𝒙 −𝟐 + 𝟐𝒙 −𝟐 =2

49−1