Year 8 Interactive Maths - Second Edition

Indices

The product 5 × 5 can be written as 5².

5 × 5 is known as the expanded form (or factor form) of 25 and 5² 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).
• 2³ is read as '2 to the power 3' or simply '2 cubed'.

That is:

Example 1

Write 4³ as a number.

Solution:

Note the following:

• 64 = 4³
• 3 is the power (or index or exponent)
• 4 is the base number
• 64 is a basic numeral or number
• 4³ is the index form (or power form) of 64
• 4 × 4 × 4 is the expanded form of 64
• For 64 = 4 × 4 × 4 = 4³, the base number 4 appears three times as a factor of the basic numeral (or number) 64
• 4³ 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