1.2 What about powers?

Most people are familiar with the fact that five multiplication five can also be written as five squared (said as ‘five squared’) and four multiplication four multiplication four as 43 (said as ‘four cubed’). This shorthand notation can be extended indefinitely, so two multiplication two multiplication two multiplication two multiplication two multiplication two becomes two super six (said as ‘two to the power of six’, or more usually as just ‘two to the six’). In this example, the 2 is called the base number and the superscript 6 (indicating the number of twos that have been multiplied together) is variously called the power, the exponent or the index (plural indices).

  • Use your calculator’s instruction booklet or your computer calculator’s help system to find out how to enter a base number raised to a power, such as two super six .

  • You may have a button labelled ‘ x super y ’, in which case you should press ‘2’ then ‘ x super y ’ then ‘6’. Alternatively you may have a button labelled ‘^’ in which case you should press ‘2’ then ‘^’ then ‘6’. In both cases you probably need to then press ‘=’ or ‘Enter’.

If you are asked to calculate, say, five multiplication three squared , another rule of precedence tells you that:

powers should be calculated before multiplication, division, addition or subtraction.

So, in the example of five multiplication three squared , the three squared should be evaluated (worked out) first.

equation sequence part 1 three squared equals part 2 three multiplication three equals part 3 nine comma so equation sequence part 1 five multiplication three squared equals part 2 five multiplication nine equals part 3 45 full stop

Question 1.3

Do the following calculations without using your calculator. Use your calculator to check the answers.

    • a. three cubed

  • equation sequence part 1 three cubed equals part 2 three multiplication three multiplication three equals part 3 27

    • b. three multiplication five squared

  • The five squared should be evaluated first, and equation sequence part 1 five squared equals part 2 five multiplication five equals part 3 25 full stop

    Then equation sequence part 1 three multiplication five squared equals part 2 three multiplication 25 equals part 3 75

    • c. two cubed multiplication three squared

  • The two cubed and three squared should be evaluated first.

    equation sequence part 1 two cubed equals part 2 two multiplication two multiplication two equals part 3 eight and equation sequence part 1 three squared equals part 2 three multiplication three equals part 3 nine full stop

    Then equation sequence part 1 two cubed multiplication three squared equals part 2 eight multiplication nine equals part 3 72

    • d. three squared plus four squared

  • The three squared and four squared should be evaluated first.

    equation sequence part 1 three squared equals part 2 three multiplication three equals part 3 nine and equation sequence part 1 four squared equals part 2 four multiplication four equals part 3 16 full stop

    Then equation sequence part 1 three squared plus four squared equals part 2 nine plus 16 equals part 3 25

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1.1 Doing calculations in the right order
Next : 1.3 The role of brackets 
1.3 The role of brackets