Algebra 1.4Powers and Exponents

Learning Targets

Language Goal Students will be able to read and say an exponential

expression.

Math Goal Students will be able to evaluate expressions containing

exponents.

Essential Questions How would you identify the results of operations exponents

and square roots?

Warm-up

Go Over Quiz

Take a look at your quiz first on your own.

Do not put it away we will go over it together

You can come in to re-take the quiz. It will be different questions but same format.

Let me know when you would want to re-take it.

Vocabulary

Power

Base

Exponent

An expression written with an exponent and a base

34The number that is used as a factor

Ex. 3 is the base

The number that indicates how many times the base is used as a factor

Ex. 4 is the exponent

Introducing Exponents

xaBase:The number that is used as a factor

Exponent:Tells how many times the base is used as a factor

We read this as “a raised to the x power”

It means…

x times

Exponent Notes

Exponents use multiplication. The base gets multiplied the number of times of the exponent.

Example:

2●2●2●2 =

16

Writing Powers for Geometric Models

Write the power represented by each geometric model

44

4

Negative Bases

Do these powers have the same value?

What will the sign be when these powers are evaluated?

When the base is negative…

(−2)3

Exponent Sign of Evaluated Power

Even  

Odd  

−22

Example 2:

1. 2. 3.

4. 5. 6.

7. 8.

Saying Exponents

xa When x is 1 we say “a raised to the first power”  When x is 2 we say “a squared”

Or you can say “a raised to the second power”  When x is 3 we say “a cubed”

Or you can say “a raised to the third power”

When we are working with exponents we do not say “to the ten power” or “to the four power.”Instead we say “to the tenth power” and “to the fourth power.”

Practice writing out the words for how you would say out loud the following powers.

1. ___________ to the _____________ power

2. __________________________________________

3. __________________________________________

4. __________________________________________

5. _________________________________________

6. __________________________________________

Special Exponents

Whenever x is zero, what is the value of our number?

Example:

Whenever x is 1, what is the value of our number?

Example

Expanded Form and Standard Form

Example Problem:

Expanded form: 6●6●6

Standard form: 216

Practice

Find the value of these exponents. Write them in standard and expanded form!

Exponent Form Expanded Form Standard Form

1.    

2.    

3.    

4.    

5.    

6.    

7.    

8.    

9.    

10.    

64

2980

15

92

70

(−8)3

92341

10

123

−302

Example 3:

Writing a Number as a Power of a Given Base

Ex. 8 is a power of 2 because

Let’s Try: Write 81 as a power of 3.

Example 3:

You try:

1. Write 16 as a power of 4.

2. Write -27 as a power of (-3)

3. Write 1,000 as a power of 10.

4. 225; Base (-15)

Guided Practice:

Try page 29 #2, 6, 11

Guided Practice

Reading Strategies

Reading Strategies

Lesson Quiz