Powers
(KS3, Year 7)

The Lesson

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

Saying a Power

How do you say 32? You could say:
  • 3 to the power of 2.
  • The second power of 3.
  • 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 = 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 base? What is an exponent?