1. 1-4 Powers and Exponents Warm Up Lesson Presentation Lesson Quiz
Holt Algebra 1
Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal Algebra 1

2. Warm Up Simplify. 1. 2(2) 2. (–2)(–2) 3. (–2)(–2)(–2) 4 4. 3(3)(3) 4–8 27 4 9 5.

3. Objective
Simplify expressions containing exponents.

4. Vocabulary
power
base
exponent

5. 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 is
used as a factor. 3 2
The exponent, 2 tells
how many times the
base, 3, is used as a
factor.

6. 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. S
When a number is raised to the third power, we usually say it is “cubed.” The of volume of a cube is s  s  s = s3 where s is the side length. S

7. 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 5 53
The factor 5 is used 3 times.

8. Example 1B: Writing Powers for Geometric Models
Write the power represented by the geometric model. 6
The figure is 6 units long and 6 units wide. 6 x 6 6 62
The factor 6 is used 2 times.

9. 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 22
The factor 2 is used 2 times. x b.
The figure is x units long, x units wide, and x units tall. x  x  x x
The factor x is used 3 times. x3

10. 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.
Reading Exponents
Words
Multiplication
Power
Value
3 to the first power 3 31 3
3 to the second power, or 3 squared
3  3 32 9
3 to the third power, or 3 cubed
3  3  3 33 27
3 to the fourth power 34
3  3  3  3 81
3 to the fifth power
3  3  3  3  3 35
243

11. Caution!
In the expression –52, 5 is the base because the negative sign is not in parentheses. In the expression (–2)2, –2 is the base because of the parentheses.

12. Example 2: Evaluating Powers
Evaluate 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. Find the product of –1 and
two 10’s.
–1 • 10 • 10
–100

13. Example 2: Evaluating Powers
Evaluate the expression. C. 2 9 
Use as a factor 2 times. 2 9 = 4 81 2 9 

14. Example 3: Writing Powers
Write each number as a power of the given base.
A. 64; base 8
8  8
The product of two 8’s is 64. 82
B. 81; base –3
(–3)(–3)(–3)(–3)
The product of four –3’s is 81.
(–3)4

15. Check It Out! Example 2
Simplify each expression.
a. (–5)3
(–5)(–5)(–5)
Use –5 as a factor 3 times.
–125
b. –62
Think of a negative sign in front of a power as multiplying by –1.
–1  6  6
Find the product of –1 and
two 6’s.
–36

16. Check It Out! Example 2
Simplify each expression. c.
Use as a factor 3 times. 3 4 27 64

17. 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 8’s is 64. 82
b. –27; base –3
(–3)(–3)(–3)
The product of three (–3)’s is –27.
–33

18. 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?
Understand the problem 1
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.

19. Example 4 Continued 2
Make a Plan
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

20. Notice that after each round of calls the
Example 4 Continued
Solve 3
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.
34 = 3  3  3  3 = 81
Multiply four 3’s.
In the fourth round of calls, 81 families
will have been contacted.

21. Example 4 Continued
Look Back 4
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.

22. 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. 28
2  2  2  2  2  2  2  2
Multiply eight 2’s.
256
The product of eight 2’s.

23. n n Lesson Quiz 1. Write the power represented by the geometric model.
Simplify each expression.
3. –63
−216 2.
4. 6
216
5. (–2)6 64
Write each number as a power of the given base.
; base 7 73
7. 10,000; base 10
104