Bases and Exponents

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​✔👇Important Info ✔👇

​Learning Target: I can write and solve problems with exponents.

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Vocabulary: base, exponent, power, squared, cubed​

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Standard: CC.2.2.6.B.1 Apply and extend previous understandings of arithmetic to algebraic expressions.​

Essential Question: How do exponents show repeated multiplication?

Expectations for Participation

​In order to earn credit for this virtual lesson you should:  

• Listen and follow along.  Do not do other activities during class.

• Answer all interactive questions in the activity.  Be ready to fix errors or respond to questions.

• Participate appropriately in chat pod.

• Raise your hand and wait to be called on to unmute.

• Try your best!

​Have you ever seen these small little numbers in math? Have you ever wondered what they mean?

​4³

​These smaller numbers are called exponents and they mean repeated multiplication!

​= 4 x 4 x 4

​4³

​When we read an expression that contains an exponent, we say "eight to the 3rd power" or "eight to the power of 3".

​The base is the number being multiplied by itself. The exponent is how many times it is being multiplied!

​Take a look at the different forms for expressions with exponents.

​

Standard form shows the answer once it is evaluated.

​How would you write this repeated multiplication using an exponent?

​

10 x 10 x 10 x 10 x 10​

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​How would you write this repeated multiplication using an exponent?

​

10 x 10 x 10 x 10 x 10​ =

​

​10⁵

​Remember, 10 is the base and 5 is the exponent.

Multiple Choice

Write 6 x 6 x 6 x 6 using an exponent.

• 4⁶

• 6⁴

• 24

• 6 x 4

Multiple Choice

What is 4³ in expanded form?

• 12

• 64

• 4 x 4 x 4

• 4 x 4

Multiple Choice

The base number in 3⁵ is

• 3

• 5

Multiple Choice

Find the equivalent expression for

15 × 15 × 15 × 15

• 15⁴

• 4¹⁵

• 15 x 4

• 15 + 15 + 15 + 15

Multiple Choice

The exponent in 4² is

• 4

• 2

Multiple Choice

2⁵ is the same as 2 x 5

• True

• False

​Squared and Cubed

​When you raise a base to the 2nd power, sometimes we call that "squaring" the number. It means we multiply by itself.

​

When we raise a base to the 3rd power, sometimes we call that "cubing"the number. It means the base is multiplied by itself three times.​

​5²

​5³

Multiple Choice

"Six cubed" is the same as ___________.

• 6²

• 6³

• 6⁴

• 6¹

Multiple Choice

"Four squared" is the same as _________.

• 4²

• 4³

• 4⁴

• 4¹

Multiple Choice

What operation is used to "square a number"?

• Division

• Subtraction

• Multiplication

• Addition

​Now that we know what exponents are, it is time for us to get ANSWERS to these problems!

​

A calculator can be a helpful tool when evaluating exponents because the numbers can get very large!

​

I will show you a few different online calculators that can help you get answers to these problems.​

​Calculator Options

​You can always put the repeated multiplication into the calculator like this: 5 x 5 x 5 x 5 but sometimes there are short cut keys to make your life easier!

​Calculator Options

Here is the Desmos Scientific Calculator:

​Type the base number 5.

Then use the a^b button.

Enter the exponent 4.

The answer will appear on the right side of the calculator display.

​TI-83 Calculator

​6^4 is another way!

(^ is called a carat)​

​Where do the answers on the calculator come from?

​

​

​

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​It is time for you to get a calculator! You will have 4 questions to answer coming up next!

​

​

Multiple Choice

5² = ?

"Five squared equals what number?"

• 10

• 15

• 20

• 25

Multiple Choice

What is 1⁵ ?

"One to the fifth power"

• 15

• 5

• 1

• 0

Multiple Choice

What is 10³ ?

"Ten to the 3rd power" or "ten cubed".

• 100

• 30

• 300

• 1000

Multiple Choice

A scientist reports that a bacteria culture contains 3³ bacteria.

How many bacteria is that?

• 33

• 9

• 18

• 27

​CHALLENGE AREA!

​Let's look at this graphic to figure out exponents of zero and one. Sometimes these can be tricky!

Multiple Choice

What is 100⁰ ?

• 0

• 100

• 1

• 1000

Multiple Choice

3⁴ is larger than 4³.

• True

• False

Multiple Choice

Evaluate $$x^3$$ for $$x=5$$

• 5

• 125

• 15

• 53

Poll

How are you feeling about exponents?

Do you understand them?