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Holt Algebra 1
1-4 Powers and Exponents1-4 Powers and Exponents
Holt Algebra 1
Warm Up
Lesson Presentation
Lesson Quiz
Holt Algebra 1
1-4 Powers and Exponents
Warm Up
Simplify.
1. 2(2)
2. (–2)(–2)
3. (–2)(–2)(–2)
4. 3(3)(3)
4
4
–8
27
49
5.
Holt Algebra 1
1-4 Powers and Exponents
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 base is the
number that isused as a factor.
32 The exponent, 2 tells
how many times thebase, 3, is used as afactor.
Holt Algebra 1
1-4 Powers and Exponents
When a number is raised to the second power, we usually say it is “squared.” The area of a square is s s = s2, is the side length.
S
S
When a number is raised to the third power, we usually say its “cubed.” The of volume of a cube is s s s = s3 is the side length.
S
SS
Holt Algebra 1
1-4 Powers and Exponents
Write the power represented by the geometric model.
55
5 The figure is 5 units long, 5 units wide, and 5 units tall. 5 5 5
The factor 5 is used 3 times.53
Example 1A: Writing Powers for Geometric Models
Holt Algebra 1
1-4 Powers and Exponents
Write the power represented by the geometric model.
The figure is 6 units long and 6 units wide. 6 x 6
The factor 6 is used 2 times.62
6
6
Example 1B: Writing Powers for Geometric Models
Holt Algebra 1
1-4 Powers and Exponents
Write the power represented by each geometric model.
a.
22
b.
Check It Out! Example 1
x
x
x
The figure is 2 units long and 2 units wide. 2 2
The factor 2 is used 2 times.
The figure is x units long, x units wide, and x units tall. x x x
The factor x is used 3 times.x3
Holt Algebra 1
1-4 Powers and Exponents
There are no easy geometric models for numbers raised to exponents greater than 3, but you can still write them using repeated multiplication or a base and exponent.
3 to the second power, or 3 squared
3 3 3 3 3
Multiplication Power ValueWords
3 3 3 3
3 3 3
3 3
33 to the first power
3 to the third power, or 3 cubed
3 to the fourth power
3 to the fifth power
3
9
27
81
243
31
Reading Exponents
32
33
34
35
Holt Algebra 1
1-4 Powers and Exponents
Caution!In the expression –52, 5 is the base because the negative sign is not in parentheses. In the expression (–2), –2 is the base because of the parentheses.
Holt Algebra 1
1-4 Powers and Exponents
Evaluate each expression.
A. (–6)3
(–6)(–6)(–6)
–216
B. –102
–1 • 10 • 10
–100
Use –6 as a factor 3 times.
Find the product of –1 and
two 10’s.
Example 2: Evaluating Powers
Think of a negative sign in front of a power as multiplying by a –1.
Holt Algebra 1
1-4 Powers and Exponents
Use as a factor 2 times.2 9
Evaluate the expression.
C.
29
29
Example 2: Evaluating Powers
= 4
81 29
29
Holt Algebra 1
1-4 Powers and Exponents
Evaluate each expression.
a. (–5)3
b. –62
Check It Out! Example 2
(–5)(–5)(–5) Use –5 as a factor 3 times.
–125
–1 6 6
–36
Think of a negative sign in front of a power as multiplying by –1.
Find the product of –1 andtwo 6’s.
Holt Algebra 1
1-4 Powers and Exponents
Check It Out! Example 2
Evaluate the expression.
c.
Use as a factor 3 times.34
2764
Holt Algebra 1
1-4 Powers and Exponents
Write each number as a power of the given base.
A. 64; base 8
8 8
82
B. 81; base –3
(–3)(–3)(–3)(–3)
(–3)4
The product of two 8’s is 64.
The product of four –3’s is 81.
Example 3: Writing Powers
Holt Algebra 1
1-4 Powers and Exponents
Write each number as a power of a given base.
a. 64; base 4
b. –27; base –3
Check It Out! Example 3
4 4 4 The product of three 4’s is 64.
43
(–3)(–3)(–3)
–33
The product of three (–3)’s is –27.
Holt Algebra 1
1-4 Powers and Exponents
In case of a school closing, the PTApresident calls 3 families. Each of these families calls 3 other familiesand so on. How many families will have been called in the 4th round of calls?
The answer will be the number of familiescontacted in the 4th round of calls.
Example 4: Problem-Solving Application
Understand the problem1
List the important information:
• The PTA president calls 3 families.
• Each family then calls 3 more families.
Holt Algebra 1
1-4 Powers and Exponents
Draw a diagram to show the number of
Families called in each round of calls.
2 Make a Plan
Example 4 Continued
2nd round of calls
1st round of calls
PTA President
Holt Algebra 1
1-4 Powers and Exponents
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
So, in the 4th round of calls, 34 families will have
been contacted.
34 = 3 3 3 3 = 81 Multiply four 3’s.
In the fourth round of calls, 81 families will have been contacted.
2nd round of calls: 3 3 = 9 or 32 families contacted
3rd round of calls: 9 3 = 27 or 33 families contacted
Solve3
Example 4 Continued
Holt Algebra 1
1-4 Powers and Exponents
Drawing a diagram helps you visualize the
problem, but the numbers become toolarge for a diagram. The diagram helps you recognize the pattern of multiplying by 3 so that you can write the number as apower of 3.
Look Back4
Example 4 Continued
Holt Algebra 1
1-4 Powers and Exponents
What if…? How many bacteria will be on the slide after 8 hours?
Check it Out! Example 4
28After each hour, the number of bacteria is a power of 2.
2 2 2 2 2 2 2 2 Multiply eight 2’s.
The product of eight 2’s.256