Powers
(KS3, Year 7)

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 Parts of a Power

A power consists of a base and an exponent:

• 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 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: 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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