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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