Powers (Mathematics Glossary)
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:
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
3 is called the base. It is the number that is multiplying itself.
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.
The base can be a letter instead of a number:
The exponent can be a letter:
Both the base and the exponent can be letters:
Saying a Power
How do you say 32?
You could say:
3 to the power of 2.
The second power of 2.
3 to the 2.
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:
102 = 10 × 10 = 100
103 = 10 × 10 × 10 = 1000
103 = 10 × 10 × 10 × 10 = 10000
Notice that the exponent tells you how many 0s there are after the 1.
Powers of 10 are useful for scientific notation.