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Bases in Powers (Mathematics Glossary)

What Is a Base in a Power?

The base is of a power is the number (or other quantity) that is multiplied by itself.

Dictionary Definition

The Merriam-Webster dictionary defines a base as "a number (such as 5 in 56.44 or 57) that is raised to a power."

Understanding Bases in Powers

A power is the product of multiplying a number by itself. A power consists of a base and an exponent.

For example, 32 is a power. 3 is the base and 2 is the exponent.

3 squared

This means that 3 (the base) is multiplied by itself 2 (the exponent) times.

3 squared equals 3 times 3

Real Examples of Bases in Powers

Some real examples of bases in powers are given below.

  • The power below has a base of 4:

    4 to the power of 3
  • The power below has a base of 2:

    2 to the power of 4
  • The base can also be a letter. The power below has a base of a:

    a to the power of 3
Curriculum
Algebra Lessons
Interactive Test
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Here's a second test on bases in powers.
Here's a third test on bases in powers.

Note

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.