Math 6 NOTES (4.1)
Name: _________________________________
Bases, Exponents & Powers

Bases & Exponents
2
BASE: the common
_____________
4
EXPONENT: tells you how
many times the _____________
is being multiplied by itself.
24 = 2 • 2 • 2 • 2 = 16
 Powers – numbers expressed using _________________.
Math the symbols to the correct wording:
Symbols
Words
50 ______
A) Eight to the third power; eight cubed
61______
B) Nine to the fourth power
72______
C) Five to the power of zero
83______
D) Seven to the second power; seven squared
94______
E) Six to the first power
Let’s Practice… Write each power as a product of the same factor:
1)
84
____________________________________
2)
46
____________________________________
3)
25
____________________________________
4)
103
____________________________________
Write each expression in exponential form:
5)
9•9•9•9•9•9
____________________________________
6)
5•5•5
____________________________________
7)
1
1
1 1
• •
•
3
3
3 3
____________________________________
Evaluate (solve)
73
8)
9)
____________________________________
35
____________________________________
81
10)
____________________________________
 Powers of 10
Do you see a pattern?
101
=
10
=
10
The exponent represents the number
of zeros in the product.
102
=
10 x 10
=
100
103
=
10 x 10 x 10 =
For example:
1014 = The number 1 with 14 zeros
(100,000,000,000,000)
You try:
1,000
Write as the product of common factors AND evaluate
104 ________________________________

100
=
_______________
What about a number raised to the power of zero? Complete the pattern:
23 = 8
22 = 4
Do you see a pattern?
Divide by the base as the powers
decrease.
21 = 2
20 = _____
*Any number to the zero power equals _______ !
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and Intervention
Powers and Exponents
Exponent
Base
3 ⭈ 3 ⭈ 3 ⭈ 3 ⫽ 81
兵
34 ⫽
common factors
The exponent tells you how many times to use the base as a factor.
Write 63 as a product of the same factor.
The base is 6. The exponent 3 means that 6 is used as a factor 3 times.
63 ⫽ 6 ⭈ 6 ⭈ 6
Evaluate 54.
54 ⫽ 5 ⭈ 5 ⭈ 5 ⭈ 5
⫽ 625
Write 4 ⭈ 4 ⭈ 4 ⭈ 4 ⭈ 4 in exponential form.
The base is 4. It is used as a factor 5 times, so the exponent is 5.
4 ⭈ 4 ⭈ 4 ⭈ 4 ⭈ 4 ⫽ 45
Write each power as a product of the same factor.
1. 73
2. 27
3. 92
4. 154
7. 104
8. 50
Evaluate each expression.
5. 35
6. 73
Write each product in exponential form.
9. 2 ⭈ 2 ⭈ 2 ⭈ 2
10. 7 ⭈ 7 ⭈ 7 ⭈ 7 ⭈ 7 ⭈ 7
11. 10 ⭈ 10 ⭈ 10
12. 9 ⭈ 9 ⭈ 9 ⭈ 9 ⭈ 9
13. 12 ⭈ 12 ⭈ 12
14. 5 ⭈ 5 ⭈ 5 ⭈ 5
15. 6 ⭈ 6 ⭈ 6 ⭈ 6 ⭈ 6
16. 1 ⭈ 1 ⭈ 1 ⭈ 1 ⭈ 1 ⭈ 1 ⭈ 1 ⭈ 1
© Glencoe/McGraw-Hill
6
Mathematics: Applications and Concepts, Course 2