Index notation
is a short way of writing repeated multiplication of the same base.
When the same number is multiplied by itself several times, we write it using a power (also called an index or exponent). The lower number is the base, and the small raised number is the index — it counts how many times the base is being multiplied.
So means with copies of . For example .
Two special names you will use often:
- is read 'a squared' (because the area of a square with side is ).
- is read 'a cubed' (because the volume of a cube with side is ).
Anything to the power is just the number itself: . And for any non-zero base — a result you will meet again with the division law of indices.
- means multiplied by itself times.
- The base is the number being multiplied; the index counts the copies.
- is 'a squared'; is 'a cubed'.
- and (for any non-zero ).