Powers of Ten and Exponents - Basic Mathematics for Water and Wastewater Operators - page 107

6 Powers of Ten

and Exponents

10 6 = 10 × 10 × 10 × 10 × 10 × 10 = 1,000,000

RULES
When working with powers and exponents, the following key points are important:

1. Powers are used to identify area , as in square feet, and volume, as in cubic
feet .

2. Powers can also be used to indicate that a number should be squared, cubed,
etc. This later designation is the number of times a number must be multi-
plied by itself. When several numbers are multiplied together, such as 4 × 5
× 6 = 120, the numbers, 4, 5, and 6 are the factors ; 120 is the product .

3. If all of the factors are alike, such as 4 × 4 × 4 × 4 = 256, the product is
called a power . Thus, 256 is a power of 4, and 4 is the base of the power. A
power is a product obtained by using a base a certain number of times as a
factor.

4. Instead of writing 4 × 4 × 4 × 4, it is more convenient to use an exponent to
indicate that 4 is to be used as a factor four times. This exponent, a small
number placed above and to the right of the base number, indicates how
many times the base is to be used as a factor. Using this system of notation,
the multiplication 4 × 4 × 4 × 4 is written as 4 4 . The superscript 4 is the
exponent, showing that 4 is to be used as a factor 4 times.

5. This same idea can also be applied to letters ( a , b , x , y , etc.); for example,

z 2 = z × z

z 4 = z × z × z × z

Note: When a number or letter does not have an exponent, it is considered to
have an exponent of one.

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