Warm Up

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Preview
Warm Up
California Standards
Lesson Presentation
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Warm Up Simplify. 1. 2(2) 2. (2)(2) 3.
(2)(2)(2) 4. 3(3)(3)
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4
8
27
5.
3

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Vocabulary
power base exponent
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A power is an expression written with an exponent
and a base or the value of such an expression. 3²
is an example of a power.
The exponent, 2, tells how many times the base,
3, is used as a factor.
The base, 3, is the number that is used as a
factor.
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When a number is raised to the second power, we
usually say it is squared. The area of a
square is s ? s s2, where s is the side length.
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Additional Example 1A Writing Powers for
Geometric Models
Write the power represented by the geometric
model.
The figure is 5 units long, 5 units wide, and 5
units tall. 5 ? 5 ? 5
The factor 5 is used 3 times.
53
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Additional Example 1B Writing Powers for
Geometric Models
Write the power represented by the geometric
model.
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The figure is 6 units long and 6 units wide. 6 x
6
6
62
The factor 6 is used 2 times.
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Check It Out! Example 1
Write the power represented by each geometric
model.
a.
The figure is 2 units long and 2 units wide. 2 ?
2
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The factor 2 is used 2 times.
b.
The figure is x units long, x units wide, and x
units tall. x ? x ? x
The factor x is used 3 times.
x3
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There are no easy geometric models for numbers
raised to exponents greater than 3, but you can
still write them using repeated multiplication or
with a base and exponent.
Reading Exponents
Words
Power
Value
Multiplication
3 to the first power
3
3
31
3 to the second power, or 3 squared
32
3 ? 3
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3 to the third power, or 3 cubed
3 ? 3 ? 3
27
33
81
3 ? 3 ? 3 ? 3
3 to the fourth power
34
35
3 ? 3 ? 3 ? 3 ? 3
243
3 to the fifth power
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Additional Example 2 Evaluating Powers
Simplify each expression.
A. (6)3
(6)(6)(6)
Use 6 as a factor 3 times.
216
B. 102
Think of a negative sign in front of a power as
multiplying by a 1.
1 10 10
Find the product of 1 and two 10s.
100
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Additional Example 2 Evaluating Powers
Simplify the expression. C.
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Check It Out! Example 2
Simplify each expression.
a. (5)3
(5)(5)(5)
Use 5 as a factor 3 times.
125
Think of a negative sign in front of a power as
multiplying by 1.
b. 62
1 ? 6 ? 6
Find the product of 1 and two 6s.
36
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Check It Out! Example 2
Simplify the expression. c.
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Additional Example 3 Writing Powers
Write each number as a power of the given base.
A. 64 base 8
8 ? 8
The product of two 8s is 64.
82
B. 81 base 3
(3)(3)(3)(3)
The product of four 3s is 81.
(3)4
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Check It Out! Example 3
Write each number as a power of a given base.
a. 64 base 8
8 ? 8
The product of two 8s is 64.
8²
b. 27 base 3
(3)(3)(3)
The product of three 3s is 27.
(3)3
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Additional Example 4 Problem-Solving Application
In case of a school closing, the PTA president
calls 3 families. Each of these families calls 3
other families, and so on. How many families will
have been called in the 4th round of calls?
The answer will be the number of
families contacted in the 4th round of calls.
List the important information The PTA
president calls 3 families. Each family then
calls 3 more families.
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Additional Example 4 Continued
Draw a diagram to show the number of families
called in each round of calls.
PTA President
1st round of calls
2nd round of calls
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Additional Example 4 Continued
Notice that after each round of calls the number
of families contacted is a power of 3.
1st round of calls 1 ? 3 3 or 31 families
contacted
2nd round of calls 3 ? 3 9 or 32 families
contacted
3rd round of calls 9 ? 3 27 or 33 families
contacted
So, in the 4th round of calls, 34 families will
have been contacted.
Multiply four 3s.
34 3 ? 3 ? 3 ? 3 81
In the fourth round of calls, 81 families will
have been contacted.
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Additional Example 4 Continued
Drawing a diagram helps you visualize the
problem, but the numbers become too large for a
diagram. The diagram helps you recognize the
pattern of multiplying by 3 so that you can
write the number as a power of 3.
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Check It Out! Example 4
What if? How many bacteria will be on the slide
after 8 hours?
After each hour, the number of bacteria is a
power of 2.
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2 ? 2 ? 2 ? 2 ? 2 ? 2 ? 2 ? 2
Multiply eight 2s.
256
The product of eight 2s.
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Lesson Quiz
n
1. Write the power represented by the geometric
model.
n2
n
Simplify each expression.
3. 63
-216
2.
5. (2)6
4. 6?
216
64
Write each number as a power of the given base.
6. 343 base 7
7. 10,000 base 10
73
104