## Notation

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

### Multiplication

In algebra, the × sign is usually omitted.

For example, 3 × x is written as 3x.

If a and b are numbers then their product is a × b. This is written as ab.

The commutative law tells us that ab = ba, but we generally write algebraic expressions with the pronumerals in alphabetical order. Similarly, if there is a number in the expression, it is written first.

For example, x × z × 7 × y is written as 7xyz.

### Division

The division sign ÷ is rarely used in algebra.

We can write 24 ÷ 6 as \(\dfrac{24}{6}\). In a similar way, we use the notation \(\dfrac{x}{5}\) for 'x divided by 5'.

### 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 × z × z = z^{6}

Note that x^{0} = 1, x ≠ 0.

### Order of operations

The order in which operations are performed can also make a difference when operations are mixed, even if we are only combining addition and multiplication.

For example

2 + (3 × 4) ≠ (2 + 3) × 4 and a + (b × c) ≠ (a + b) × c

All ambiguity could be removed by using parentheses to indicate the order in which operations are to be performed. The following conventions are used to simplify the appearance of expressions.

- Evaluate expressions inside brackets first.
- In the absence of brackets, carry out operations in the following order:

- powers
- multiplication and division from left to right
- addition and subtraction from left to right.

So 3 + 2 × 6 means 3 + (2 × 6) and a + b × c means a + (b × c) = a + bc.