Transcript 3 3 3 3 3 - SchoolNotes

“Powers and Exponents”
Monday, September 20th
Write the date, and each problem from the “Do
Now” in your math notebooks.
Do Now: Part 1
Simplify.
1. 2  2  2
8
2. 3  3  3  3
81
3. 5  5  5
4. 4  4  4
125
64
5. 6  6  6  6  6
7,776
Do Now: Part 2
Copy the following study team guidelines into your Math
notebooks
Study Team Guidelines
1.Each member of the study team is responsible for his or
her own behavior.
2.Each member of the study team must be willing to help
any other team member who asks for help.
3.When you have a question, ask your team or partner
first. If no member of your team can answer, then ask
the teacher for help.
4.All partner and team talk must remain focused on the
learning we are doing. Save non academic talk for outside
the classroom!
5.Use your team voice.
Learning Target:
I can name the parts of a power
expression and evaluate exponents.
Powers and Exponents
A simple way to think of exponents and
powers is as repeated multiplication
m • m • m = m3
Key Terms
o factor: when two or more numbers are multiplied
together, each number is called a factor
o exponent: an exponent tells how many times a number
(called a base) is used as a factor
o power: a number that is expressed using a base and
an exponent
base
4
3
exponent
Powers and Exponents
4 = 4  4  4 = 64
3
Evaluating Powers
Find each value.
A. 44
44 = 4  4  4  4
= 256
B. 73
73 = 7  7  7
Use 4 as a factor 4 times.
Use 7 as a factor 3 times.
= 343
C. 191
191 = 19
Use 19 as a factor 1 time.
Evaluating exponents
43
Use 4 as a factor 3 times
4  4  4 = 16
72
Use 7 as a factor 2 times
7  7 = 49
27
Use 2 as a factor 7 times
2  2  2  2  2  2  2 = 128
35
Use 3 as a factor 5 times
3  3  3  3  3 = 243
106
Use 10 as a factor 6 times
10  10  10  10  10  10 = 1,000,000
171
Use 17 as a factor 1 time
171 = 17
Exponents
To express a whole number as a power, write the
number as the product of equal factors. Then
write the product using the base and an exponent.
For example, 10,000 = 10  10  10  10 = 104.
Expressing Whole Numbers as Powers
Write each number using an exponent and the given
base.
A. 625, base 5
625 = 5  5  5  5
5 is used as a factor 4 times.
= 54
B. 64, base 2
64 = 2  2  2  2  2  2
= 26
2 is used as a factor 6
times.
Write each number using an exponent and the given base
343, base 7
7  7  7 = 73
256, base 2 2 2 2 2 2 2 2 2 = 28
1,000,000,000 base 10
10 10 10 10 10 10 10 10 10 = 109
Application
On Monday, Erik tells 3 people a secret. The next
day each of them tells 3 more people. If this
pattern continues, how many people besides Erik will
know the secret on Friday?
On Monday, 3 people know the secret.
On Tuesday, 3 times as many people know as those
who knew on Monday.
On Wednesday, 3 times as many people know as
those who knew on Tuesday.
On Thursday, 3 times as many people know as those
who knew on Wednesday.
Application: Continued
On Friday, 3 times as many people know as those
who knew on Thursday.
Each day the number of people is 3 times greater.
3  3  3  3  3 = 35 = 243
On Friday 243 people besides Erik will know the
secret.
Scientists and mathematicians use exponential notation
To describe very large and very small numbers.
The average distance between the earth and the sun is
1 AU (astronomical unit) or about 93 million miles.
We can write that number as
• Ninety three million
•93,000,000
•93 x 106
What advantage is there in using exponential
notation to write very large numbers?
Quick Write:

Today I learned …
Tonight’s Homework
(due: Tuesday, 9/21)
In your text book:


Read: pg. 10-11
Do: pg. 12-13; #16-22, 3135 and 48