An exponent can be defined as a way of presenting numbers in terms of powers. Specifically, the exponent number determines how many times a specific base number is multiplied by itself.
Whole Number Exponents
Below are examples of how numbers with exponents can be converted to whole numbers. The top image on the right also displays how to work through a problem with an exponent.
- 52 = 25
- 44 = 256
- 103 = 1,000
- 45,1311 = 45,131
Fraction Exponents
Exponents presented as a fraction of 1 divided by a number perform a root function whereby a base number is reduced by the root designated by the denominator in the exponent. See the middle image.
Here are some examples of how numbers with fraction exponents can be converted to a whole number:
- 161/4 = 2
- 641/2 = 8
- 100001/4 = 10
- 2161/3 = 6
Negative Exponents
When exponents are expressed as negative, the base number is multiplied by itself the number of times as denoted by the exponent number. However, that calculated value is used to divide the number one, thereby creating a fraction. Refer to the bottom image.
The primary application uses a base number of ten which provides calculations useful for the metric system of measure (discussed later). Here are some examples of how numbers with negative exponents can be converted:
- 10-3 = 0.001
- 10-4 = 0.0001
- 10-5 = 0.00001
- 10-1 = 0.1
