# Powers(KS3, Year 7)

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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:

## 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 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:

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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