Content description

Apply index laws to numerical expressions with integer indices (ACMNA209)
Source: Australian Curriculum, Assessment and Reporting Authority (ACARA)

Index notation

Powers (or indices) provide a useful way for writing the product of repeated factors.

• A power is the product of a certain number of factors, all of which are the same.
  For example, 2\(^4 = 2 × 2 × 2 × 2\) is the fourth power of 2.
• The number 2 in 2\(^4\) is called the base.
• The number 4 in 2\(^4\) is called the index or exponent.
• For any number b, b\(^1\) = b.
• In general, \(b^n = \underbrace{{b × b × b ×………..×\ b}}_n\), where there are n factors in the product.
  Here b is called the base and n the index.

Example 1

1. \(3 × 3 × 3 × 7 × 7 × 7 × 7 = 3^3 × 7^4\)
2. \begin{align}81 &= 3 × 3 × 3 × 3\\ &= 3^4\end{align}

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