Key learning points

1. When multiplying two terms, you can sometimes write this more simply.
2. If the powers have the same base, then the powers can be combined into a single power.
3. The exponent or index of the new power reflects this combination.
4. By studying the structure of multiplication, you can see how the index will change.
5. a^b × a^c = a^(b+c)

Common misconception

Keywords

• Power - 16 is the fourth power of 2. Alternatively this can be written as 2^4 which is read as “2 to the power of 4”.

• Index - An exponent is a number positioned above and to the right of a base value. It indicates repeated multiplication. An alternative word for this is index (plural indices).

• Coefficient - A numerical coefficient is a constant multiplier of the variables in a term.

• Commutative - An operation is commutative if the values it is operating on can be written in either order without changing the calculation.

• Associative - An operation is associative if a repeated application of the operation produces the same result regardless of how pairs of values are grouped.