Bases in Powers
(KS3, Year 7)

The Lesson

The base 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

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.
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See Also

What is a power? What is an exponent?