Year 8 Interactive Maths  Second Edition 

5 × 5 = 25
The product 5 × 5 can be written as 5^{2}.
5 × 5 is known as the expanded form (or factor form) of 25 and 5^{2} is known as the index form of 25.
Generally when a number is multiplied by itself any number of times, the expression is simplified by using the index notation.
Note:
 2 is called the base.
 3 is called the index or power (or exponent) because it indicates the power to which the base, 2, is raised.
 8 is the basic numeral (or number).
 2^{3} is read as '2 to the power 3' or simply '2 cubed'.
That is:
Example 1
Write 4^{3} as a number.
Solution:
Note the following:
 64=4^{3}
 3 is the power (or index or exponent)
 4 is the base number
 64 is a basic numeral or number
 4^{3} is the index form (or power form) of 64
 4 × 4 × 4 is the expanded form of 64
 For 64=4 × 4 × 4 = 4^{3}, the base number 4 appears three times as a factor of the basic numeral (or number) 64
 4^{3} is read as '4 to the power 3' or simply '4 cubed'
Example 2
Write each of the following expanded forms in index form:
Solution:
Example 3
Write each of the following in expanded form:
Solution:
Example 4
Find the value of the following:
Solution:
Example 5
Write 16 in index form using base 2.
Solution:
Example 6
Write the following numbers as a product of prime factors:
Solution:
Key Terms
indices, expanded form, factor form, index form, base, index, power, exponent, basic numeral, basic number
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