In algebra, there are concise ways of expressing multiplication, division and powers.

Notation for multiplication

In algebra, the × sign is usually omitted. For example:

The product 3 × x is written as 3x instead of 3 × x.

If a and b are numbers, then their product is a × b. This is written as ab. Similarly, we write 3 × a as 3a.

This is done because it looks simpler and because the multiplication sign could be confused with a letter.

Note that the number is written first. In the example above:

3 × a is written as 3a not a3.

Similarly:

x × y × z is written as xyz and x × y × z × 7 is written as 7xyz.

Notation for division

The division sign ÷ is rarely used in algebra. The alternative notation is used.

We can write 24 ÷ 6 as $$\dfrac{24}{6}.$$ In a similar way $$\dfrac{x}{6},$$ we use the notation. So x ÷ 5 is written as $$\dfrac{x}{5}$$.

Notation for powers

The expressions for powers are written as follows:

x × x is written as x$$^2$$

y × y × y is written as y$$^3$$

z × z × z × z is written as z$$^4$$

and so on.