Powers
What Is a Power?
A power is the product of multiplying a number (or other quantity) by itself.
For example, 32 is a power of 3.
32 means that 3 will be multiplied by itself 2 times:
Dictionary Definition
The Oxford English Dictionary defines a power as "a quantity obtained by multiplying a given quantity by itself one or more times, the number of times the given quantity appears as a factor of the resulting product being indicated as the exponent of that quantity."
The Parts of a Power
A power consists of a base and an exponent:
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3 is called the base. It is the number that is multiplying itself.
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2 is called the exponent. It tells you how many times the base is multiplying itself.
Real Examples of Powers
Some real examples of powers are given below. (Don't forget: the base is multiplied by itself as many times as indicated by the exponent).
Powers can contain letters (or symbols) as well as numbers.
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The base can be a letter instead of a number:
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The exponent can be a letter:
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Both the base and the exponent can be letters:
See Also
What is a base? What is an exponent?Interactive Test
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Here's a second test on powers
Note
Saying a Power
How do you say 32?
You could say:
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3 to the power of 2.
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The second power of 3.
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3 to the 2.
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In the special case where the exponent is 2, we can say 3 "squared".
Note: In the special case where the exponent is 3, as in 33, we can say 3 "cubed".
Powers of 10
A power of 10 has a base of 10 and an exponent:
101 = 10
102 = 10 × 10 = 100
103 = 10 × 10 × 10 = 1,000
103 = 10 × 10 × 10 × 10 = 10,000
Notice that the exponent tells you how many 0s there are after the 1.
Powers of 10 are useful for scientific notation.