NAME
9-1
DATE
PERIOD
Study Guide and Intervention
Powers and Exponents
Use Exponents A number that is expressed using an exponent is called a power. The
base is the number that is multiplied. The exponent tells how many times the base is used
as a factor. So, 43 has a base of 4 and an exponent of 3, and 43 = 4 · 4 · 4 = 64.
43
exponent
{
base
Lesson 9-1
power
Any number, except 0, raised to the zero power is defined to be 1.
10 = 1
Example
20 = 1
30 = 1
40 = 1
x0 = 1, x ≠ 0
50 = 1
Write each expression using exponents.
a. 10 · 10 · 10 · 10 · 10
The base is 10. It is a factor 5 times, so the exponent is 5.
10 · 10 · 10 · 10 · 10 = 105
b. (–9) · (–9) · (–9) · (–9) · (–9) · (–9)
The base is –9. It is a factor 6 times, so the exponent is 6.
(–9) · (–9) · (–9) · (–9) · (–9) · (–9) = (–9)6
c. ( p + 2)( p + 2)(p + 2)
The base is p + 2. It is a factor 3 times, so the exponent is 3.
( p + 2)( p + 2)( p + 2) = ( p + 2)3
Exercises
Write each expression using exponents.
1. 5 · 5 · 5 · 5 · 5 · 5 · 5
2. (–7)(–7)(–7)
3. 4 · 4
4. 8 · 8 · 8
5. (–2) · (–2) · (–2) · (–2)
6. (3) ∙ (3) ∙ (3) ∙ (3) ∙ (3)
7. (0.4) · (0.4) · (0.4)
8. d · d · d · d
9. m · m · m · m · m · m · m
10. x · x · y · y
Chapter 9
11. (z – 4)(z – 4)
5
1
1
1
1
1
12. 3(–t)(–t)(–t)
Glencoe Pre-Algebra
NAME
DATE
9-1
PERIOD
Study Guide and Intervention
(continued)
Powers and Exponents
Evaluate Expressions When evaluating expressions with exponents you must follow the
order of operations.
Order of Operations
1. Simplify expressions inside grouping symbols.
2. Evaluate all powers.
3. Multiply and divide in order from left to right.
4. Add and subtract in order from left to right.
Example 1
ART An artist is painting a mural that will look like a quilt square.
The mural will have an area of 82 square feet. How many square feet is this?
8 is a factor 2 times.
82 = 8 · 8
Simplify.
= 64
The area of the mural will be 64 square feet.
Example 2
Evaluate x2 – 4 if x = –6.
x2 – 4 = ( –6)2 – 4
Replace x with –6.
= ( –6)( –6) – 4
–6 is a factor 2 times.
= 36 – 4
Multiply.
= 32
Subtract.
Exercises
Evaluate each expression.
1. 73
2. 36
5. (–4)5
9. 72 · 5
6. 28
10. 42 · 52
1 4
3. (–6)3
4. (5)
7. 33 · 6
8. 83 · 9
11. (–3)2 · (–2)3
12. 82 · 63
Evaluate each expression if g = 3, h = –1, and m = 9.
13. g 5
14. 5g2
15. g2 – m
16. hm2
17. g3 + 2h
18. m + h g3
19. 4(2m – 3)2
20. –2(g3 + 1)
21. 5(h4 – m2)
Chapter 9
6
Glencoe Pre-Algebra