Lesson 1-1: Exponents

Lesson 1-1: Exponents

Students will be able to write and evaluate numerical expressions involving whole-number exponents.

You know that patterns appear when you repeatedly multiply by numbers such as 5 or 10. Today, you will learn how to efficiently represent repeated multiplication by the same number.

True or False: If you are given a number with an exponent, the exponent represents how many times the number is used as a factor.

Answer the question on the next slide.

Multiple Choice

True or False: If you are given a number with an exponent, the exponent represents how many times the number is used as a factor.

• True

• False

You know that 100 = 10 x 10. How would you write 10,000 as a product of 10s?

Answer the question on the next slide.

Multiple Choice

If 100 = 10 x 10, how would you write 10,000 as a prodcut of 10s?

• 10 x 10

• 10 x 10 x 10

• 10 x 10 x 10 x 10

• 10 x 10 x 10 x 10 x 10

Multiple Choice

How can you write 100,000 as a product of 10s?

• 10 x 10

• 10 x 10 x 10

• 10 x 10 x 10 x 10

• 10 x 10 x 10 x 10 x 10

What pattern do you see?

100 = 10 x 10

1,000 = 10 x 10 x 10

10,000 = 10 x 10 x 10 x 10

100,000 = 10 x 10 x 10 x 10 x 10

The number of 10s you multiply is the same as the number of zeroes!

 $10^8$  

• We read this as 10 to eighth power

• It means 10 is used as a factor eight times

• What number is equal to 10 to the eighth power?

Multiple Choice

What number is equal to  $10^8$  ? 

• 100,000,000

• 1,000,000,000

• 10,000,000,000

• 100,000,000,000

 $10^8$  

• This is called the exponential form of one hundred million

• In this example, the 8 is the exponent and the 10 is the base

• The exponent tells you how many times the base is used as a factor

How can you write a number using exponents?

Each place in a place-value chart has a value that is 10 times as great as the place to its right. Use this pattern to write 1,000,000 as repeated multiplication.

Consider these questions...

• How many zeroes does 1 million have?

• How many times is 10 used as a factor to get to 1 million?

• To write 1 million in exponential form, what exponent must you use with the base 10?

Multiple Choice

How many zeroes does 1 million have?

• 2

• 4

• 6

• 8

Multiple Choice

How many times is 10 used as a factor to get to 1 million?

• 4

• 6

• 8

• 10

Multiple Choice

To write 1 million in exponential form, what exponent must you use with the base 10?

• 6

• 5

• 4

• 3

Multiple Choice

How many times is 9 used as a factor in the exponent $9^8$  ?

• 7

• 8

• 9

• 10

Multiple Choice

What is the exponent in $9^8$  ?

• 8

• 9

• 10

• 11

Multiple Choice

Write 10,000 as repeated multiplication of 10s.

• 10 x 10

• 10 x 10 x 10

• 10 x 10 x 10 x 10

• 10 x 10 x 10 x 10 x 10

Multiple Choice

Write 7 x 7 x 7 x 7 in exponential form.

•  $7^4$  

•  $4^7$  

•  $2,401$  

•  $10^7$  

Multiple Choice

What would 30,000 be in expanded form?

• $3\ \times\ 10^4$

• $10\ \times3^4$

• $30,000$

• $4\ \times\ 10^3$

Multiple Choice

What is 7,000 in expanded form?

• $7\ \times10^0$

• $7\ \times\ 10^1$

• $7\ \times\ 10^2$

• $7\ \times\ 10^3$

Multiple Choice

Why would 60 be written in expanded form as $6\ \times\ 10^1$  ?

•  $10^1$  is 100 so 100 x 6 = 60

•  $10^1$  is 10 so 10 x 6 = 60

•  $10^1$  is 54 so 54 + 6 = 60

•  $10^1$  is 0 so 6 + 0 = 60

Multiple Choice

How many times would 10 be used as a factor to equal 100,000?

• 1

• 3

• 5

• 7

Multiple Choice

How many zeroes are in $10^7$  when it is written in standard form?

• 7

• 8

• 9

• 10

Let's answer some questions!

Multiple Choice

What number is the base in $4^9$  ?

• 4

• 9

Multiple Choice

What number is the base in $17^6$  ?

• 17

• 6

Multiple Choice

What number is the exponent in $31^9$  ?

• 31

• 9

Multiple Choice

What number is the exponent in $2^{100}$  ?

• 2

• 100

Multiple Choice

Write 1,000 in expanded form using exponents.

• $10^3$

• $10^5$

• $10^7$

• $10^9$

Multiple Choice

Write 1,000,000,000 in expanded form using exponents.

• $10^3$

• $10^6$

• $10^9$

• $10^{12}$

Multiple Choice

Write 7 x 7 x 7 x 7 x 7 in expanded form using exponents.

• $5^7$

• $7^5$

• $7^6$

• $700,000$

Multiple Choice

What is 841 in expanded form using exponents?

• $\left(8\times10^2\right)\ +\ \left(4\times10^1\right)\ +\left(1\ \times10^0\right)$

• $\left(8\ \times10^2\right)\ +\ \left(8\ \times10^1\right)+0$

• $\left(5\ \times10^3\right)\ +\ \left(8\ \times10^2\right)\ +\left(3\ \times10^1\right)$

Multiple Choice

 $6^2$  = ?

• 12

• 36

• 62

• 620

Multiple Choice

 $10^8$  = ?

• 100,000

• 1,000,000

• 10,000,000

• 100,000,000

Multiple Choice

 $4^3$  = ?

• 7

• 12

• 43

• 64

Multiple Choice

 $2^7$  = ?

• 124

• 128

• 132

• 136

All done!

How are you feeling?

Poll

How comfortable do you feel with the material that was covered in today's lesson?

• Great

• Okay

• Not Great

Poll

Would you like to be in a small group to receive additional instruction after today's lesson?

• YES

• NO

Poll

Would you like to receive one-on-one support?

• Yes

• No

If you would like additional support, please wait while Mrs. Yoder forms breakout rooms on the Google Meet.

If you are ready to work independently and do not want additional support, you are now free to leave the Google Meet.