Transcript 1.2 Exponents - Lake County Schools

1-2 Exponents
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
1-2 Exponents
Warm Up
Multiply.
1. 3  3  3
27
2. 4  4  4
64
3. 2  2  2  2
16
4. 5  5  5  5
625
1-2 Exponents
Problem of the Day
Replace the letters a, b, and c with the
numbers 3, 4, and 5 to make a true
statement.
2a + 2a = bc
25+ 25 = 43
1-2 Exponents
Sunshine State Standards
Prep for MA.6.G.4.1 …Calculate…the area of
circles.
Also Review of MA.5.A.6.2
1-2 Exponents
Vocabulary
exponent
base
exponential form
1-2 Exponents
An exponent tells how many times
a number called the base is used
as a factor.
A number is in exponential form
when it is written with a base and
an exponent.
Exponent
Base
3
7 = 7  7  7= 343
1-2 Exponents
Exponential Form 101
Read
“10 to the 1st power”
Multiply
10
Value
10
1-2 Exponents
Exponential Form 102
Read
“10 squared,” or
“10 to the 2nd power”
Multiply
10  10
Value
100
1-2 Exponents
Exponential Form 103
Read
“10 cubed,” or
“10 to the 3rd power”
Multiply
10  10  10
Value
1,000
1-2 Exponents
Exponential Form 104
Read
“10 to the 4th power”
Multiply
10  10  10  10
Value
10,000
1-2 Exponents
Additional Example 1: Writing Numbers in
Exponential Form
Write each expression in exponential form.
A. 5  5  5  5
54
5 is a factor 4 times.
B. 3  3  3  3  3
35
3 is a factor 5 times.
1-2 Exponents
Check It Out: Example 1
Write each expression in exponential form.
A. 7  7  7
73
7 is a factor 3 times.
B. 6  6  6  6  6  6
66
6 is a factor 6 times.
1-2 Exponents
Additional Example 2: Finding the Value of
Numbers in Exponential Form
Find each value.
A. 26
26 = 2  2  2  2  2  2
= 64
B. 45
45 = 4  4  4  4  4
= 1,024
1-2 Exponents
Check It Out: Example 2
Find each value.
A. 34
34 = 3  3  3  3
= 81
B. 25
25 = 2  2  2  2  2
= 32
1-2 Exponents
Additional Example 3: Problem Solving Application
A phone tree is used to contact families at
Paul’s school. The secretary calls 4 families.
Then each family calls 4 other families, and so
on. How many families will be notified during
the fourth round of calls?
1
Understand the Problem
The answer will be the number of families
called in the 4th round.
List the important information:
• The secretary calls 4 families.
• Each family calls 4 families.
1-2 Exponents
2
Make a Plan
You can draw a diagram to see how many
calls are in each round.
Secretary
1st round–4 calls
2nd round–16 calls
1-2 Exponents
3
Solve
Notice that in each round, the number of calls
is a power of 4.
1st round: 4 calls = 4 = 41
2nd round: 16 calls = 4  4 = 42
So during the 4th round, there will be 44 calls.
44 = 4  4  4  4 = 256
During the 4th round of calls, 256 families will
be notified.
4
Look Back
Drawing a diagram helps you see how to use
exponents to solve the problem.
1-2 Exponents
Check It Out: Example 3
A phone tree is used to contact families at
Paul’s school. The secretary calls 3 families.
Then each family calls 3 other families, and
so on. How many families will be notified
during the fourth round of calls?
1
Understand the Problem
The answer will be the number of families
called in the 4th round.
List the important information:
• The secretary calls 3 families.
• Each family calls 3 families.
1-2 Exponents
2
Make a Plan
You can draw a diagram to see how many
calls are in each round.
Secretary
1st round–3 calls
2nd round–9 calls
1-2 Exponents
3
Solve
Notice that in each round, the number of calls
is a power of 3.
1st round: 3 calls = 3 = 31
2nd round: 9 calls = 3  3 = 32
So during the 4th round, there will be 34 calls.
34 = 3  3  3  3 = 81
During the 4th round of calls, 81 families will
be notified.
4
Look Back
Drawing a diagram helps you see how to use
exponents to solve the problem.
1-2 Exponents
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
1-2 Exponents
Lesson Quiz
Write each expression in exponential form.
1. 12  12  12
123
2. 9  9  9  9  9  9  9
97
Find each value.
3. 202 400
4. 64
1,296
5. In a phone tree, each of 3 people will call 3
people, and then each of those will call 3 more.
How many people will be called during the 5th
round of calls? 243
1-2 Exponents
Lesson Quiz for Student Response Systems
1. Which of the following represents 15  15  15
in exponential form?
A. 1524
B. 1533
C. 1542
D. 1551
1-2 Exponents
Lesson Quiz for Student Response Systems
2. Which of the following represents
12  12  12  12  12  12  12 in exponential
form?
A. 1255
B. 1266
C. 1277
D. 1288
1-2 Exponents
Lesson Quiz for Student Response Systems
3. Identify the value of 402.
A. 400
B. 200
C. 1200
D. 1600
1-2 Exponents
Lesson Quiz for Student Response Systems
4. Identify the value of 54.
A. 125
B. 225
C. 625
D. 1225
1-2 Exponents
Lesson Quiz for Student Response Systems
5. Sarah opened a savings account, and
deposited $3 on the first day. Then, each day
she deposited triple the amount of the previous
day for five days. How much did she deposit on
the fifth day?
A. $9
B. $81
C. $243
D. $729