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Powers
(KS3, Year 7)
The Lesson
A power is the product of multiplying a number (or other quantity) by itself. For example, 3^{2} is a power of 3.3^{2} 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 3^{2}? 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".
Powers of 10
A power of 10 has a base of 10 and an exponent:
10^{1} = 10
10^{2} = 10 × 10 = 100
10^{3} = 10 × 10 × 10 = 1,000
10^{3} = 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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