Lesson 3 Exponents

• How does exponential notation relate to the expanded form of a number?

• How is a•b  different from a^b?

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Exponents

Poll

Which option do you think is better?

• Option A, getting 2+4+6+8...and repeating the pattern for 30 days

• Option B getting .02+.04+.8+1.6...and repeating the pattern for 30 days

• They are the same

Open Ended

Why did you pick the option you did?

Multiple Choice

How would you represent what is happening for option A? (That was the one that started with getting $2.)

• 2+4+6+8+10+12...all the way to +60

• 2⋅30

• 2(1+30)

• 2⋅2⋅3⋅4...all the way to 30

Multiple Choice

How would you represent option B? (the one that started with 2 cents)

• 2¹ +2²+2³+2⁴+2⁵ all the way to 2³⁰

• 2³⁰

• 2¹ ⋅2²⋅2³⋅2⁴⋅2⁵

• 2²+2² +2² ...27 more times

Poll

Which would you pick?

• Still A

• Still B

• Changed to A

• Changed to B

Let's add up the numbers in the sequence:

2+4+6+8+10+12+14+16+18+20+22+24+26+28+30+32+34+36+38+40+42+44+46+48+50+52+54+56+58+60=

When we add these numbers together, we get:

930

That was in dollars so option A got you $930

2³⁰=1,073,741,824 One billion seventy-three million seven hundred forty-one thousand eight hundred twenty-four

But remember that was 2 cents so we divide it by 100

which is easy since dividing by 100 means you move the decimal 2 places to the left so

1,073,741,824 pennies =$10,737,418.24 which is
Ten million seven hundred thirty-seven thousand four hundred eighteen dollars and twenty-four cents.

Fill in the Blanks

$10,737,418.24 - $930 How much more was option B than option A?

Draw

Draw the first thing you would buy with $10,737418.24

Multiple Choice

page 31

In the expression $$a^m$$ , what does the variable a represent?

• Exponent

• Coefficient

• Base

• Product

Multiple Choice

In the expression a^m, what does the variable m represent?

• Base

• Coefficient

• Product

• Exponent

Fill in the Blanks

For any nonzero whole number a, the expression a^m is the product of how many factors of a?

factors

Multiple Choice

page 33

Write 3⁶ in expanded form.

• 3 · 3 · 3 · 3 · 3 · 3

• 3 + 3 + 3 + 3 + 3 + 3

• 6 · 6 · 6

• 3⁶

Multiple Choice

page 33

Write 6 · 6 · 6 · 6 by using exponential notation.

• 6³

• 6⁴

• 6⁶

• 4⁶

Multiple Choice

page 37

What is the base in the expression 2³?

• 8

• 3

• 2

• 6

Multiple Select

How is the expression 2³ read aloud?

• Two plus three

• Two times three

• Two to the power of three

• Two divided by three

• Two cubed

Multiple Choice

How do you evaluate the expression 2³?

• Add the number 2 to itself 3 times

• Divide the number 2 by itself 3 times

• Multiply the number 2 by itself 3 times

• Subtract the number 2 from itself 3 times

Multiple Choice

Write the expression 7 multiplied by itself 4 times using exponential notation.

• 7³

• 7⁴

• 7⁵

• 7²

Multiple Choice

What is the expanded form of 4³?

• 4 + 4 + 4

• 4 · 4 · 4

• 4 · 4

• 4 + 4 + 4 + 4

Multiple Choice

Which of the following expressions is equivalent to 5⁵?

• 5 · 6

• 5 · 5

• 5 · 5 · 5 · 5 · 5

• 5 + 5 + 5 + 5 + 5

• 6 · 6 · 6 · 6 · 6

Multiple Choice

Is the statement "2³ and 2 · 3 are equivalent expressions" correct?

• Yes, because both expressions equal 6.

• No, because 2³ is 8 and 2 · 3 is 6.

• Yes, because both expressions involve the number 2 and 3.

• No, because 2³ is 6 and 2 · 3 is 9.

Multiple Choice

What is the expanded form of 7²?

• 7 + 7

• 7 * 7

• 7 + 7 + 7

• 7 * 7 * 7

Multiple Choice

How is 4⁵ written in expanded form?

• 4 + 4 + 4 + 4 + 4

• 4 * 4 + 4

• 4 * 4 * 4 * 4 * 4

• 4^4 * 4

Multiple Choice

page 38

What is the exponential notation for the expression 5 * 5 * 5 * 5 * 5?

• 5⁴

• 5⁵

• 25²

• 10⁵

Multiple Choice

Which of the following represents 10 * 10 * 10 * 10 in exponential notation?

• 10³

• 10⁴

• 100²

• 40²

Multiple Choice

page 38

How can the prime factorization of 50 be expressed using exponents?

• 2¹ * 5¹

• 2² * 5²

• 2¹ * 5²

• 2² * 5¹

Multiple Choice

What is the correct exponential notation for the prime factorization of 100?

• 2³ * 5²

• 2³ * 5¹

• 2² * 5²

• 2⁴ * 5¹

Multiple Choice

page 39

What is the result of multiplying 23.8 by 10²?

• 238

• 2,380

• 23,800

• 238,000

Multiple Choice

What is the result of multiplying 45.9 by 10³?

• 459

• 4,590

• 45,900

• 459,000

Multiple Choice

What is the result of multiplying 4.76 by 10²?

• 476

• 4,760

• 47.6

• 47,600

Multiple Choice

On the coordinate plane, where is the city hall located?

• (4, 4)

• (4, -3)

• (-4, -3)

• (-2, 4)

Multiple Choice

On the coordinate plane, where is the bike shop located?

• (4, 4)

• (4, -3)

• (-4, -3)

• (-2, 4)

Multiple Choice

On the coordinate plane, where is the school located?

• (4, 4)

• (4, -3)

• (-4, -3)

• (-2, 4)

Multiple Choice

How many blocks does Toby bike in total from school to the bike shop and then to city hall?

• 10 blocks

• 11 blocks

• 12 blocks

• 13 blocks

Multiple Choice

What is the distance between the school and the bike shop?

• |−2| + |4| blocks

• |−2| − |4| blocks

• |2| + |−4| blocks

• |2| − |−4| blocks

Multiple Choice

What is the ordered pair that represents the post office if it has the opposite x-coordinate and same y-coordinate as the city hall represented by (−4, −3)?

• (4, 3)

• (4, -3)

• (-4, 3)

• (-4, -3)

Multiple Choice

What is the next number in the pattern: 0, 0.5, 1, 1.5, 2, 2.5, ...?

• 2.75

• 3

• 3.5

• 4

Poll

How well do you understand exponents?

• I am a master!

• I think I have it.

• I have it a little.

• I am so confused!