Environmental Engineering Reference
In-Depth Information
POWERS
The powers of 1:
1
0
= 1
1
1
= 1
1
2
= 1
1
3
= 1
1
4
= 1
The powers of 10:
10
0
= 1
10
1
= 10
10
2
= 100
10
3
= 1000
10
4
= 10,000
EXAMPLES
■
Example 6.1
Problem
: How is the term 2
3
written in expanded form?
Solution
: The power (exponent) of 3 means that the base number (2) is multiplied by
itself three times:
2
3
= 2 × 2 × 2
■
Example 6.2
Problem:
How is the term (3/8)
2
written in expanded form?
Solution:
When parentheses are used, the exponent refers to the entire term within
the parentheses. Thus, in this example,
(3/8)
2
= 3/8 × 3/8
Note:
When a negative exponent is used with a number or term, a number can be
re-expressed using a positive exponent:
6
-3
= 1/6
3
11
-5
= 1/11
5
■
Example 6.3
Problem
: How is the term 8
-3
written in expanded form?
Solution:
8
-3
= 1/8
3
= 1/(8 × 8 × 8)
Note:
A number or letter such as 3
0
or
x
0
does not equal 3
×
1 or
x
×
1, but simply 1.
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