 ## 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 x2
y × y × y is written as y3
z × z × z × z × z × z = z6

Note that x0 = 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.

1. Evaluate expressions inside brackets first.
2. In the absence of brackets, carry out operations in the following order:
1. powers
2. multiplication and division from left to right
3. 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.   