Definition
Index notation
A compact power form: a base with a small raised index.
Continue from this idea into connected AXIO math.
Defining relationship
The small raised index counts equal factors of the base.
Index notation writes a power as a base with a small raised index. For a positive whole-number index, the index tells how many equal factors of the base are multiplied.
- 1
base 2 with index 3
- 2
three equal factors
- 3
product
- Base = repeated factor
- Index = number of factors
What it means
Instead of writing the same factor again and again, write it once as the base and place the count as a small raised number. In 7³, 7 is the base and 3 is the index, so the expanded multiplication is 7 × 7 × 7.
Remember it
The small raised index counts equal factors of the base.
Example
Write 4 × 4 × 4 × 4 × 4 in index notation. The factor 4 appears five times, so the answer is 4⁵.
Watch for
Index notation describes how a power is written. Exponentiation is the operation represented by that notation.
Common mix-up
4³ means 4 × 4 × 4, not 4 × 3.
Exact meaning
Index notation writes a power as a base with a small raised index. For a positive whole-number index, the index tells how many equal factors of the base are multiplied.