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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.

3 squared

32 means that 3 will be multiplied by itself 2 times:

3 squared equals 3 times 3

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:

3 squared
  • 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).

examples of powers

Powers can contain letters (or symbols) as well as numbers.

  • The base can be a letter instead of a number:

     a cubed
  • The exponent can be a letter:

    2 to the n
  • Both the base and the exponent can be letters:

    a to the n
Curriculum
Algebra Lessons
Interactive Test
  show
 

Here's a second test on powers.
Here's a third test on powers.

Note

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:

101 = 10
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.