Powers

• Using powers is a mathematical shorthand way of writing repeated multiplication using the same number.
• A power is the small floating number that goes to the right of a number or letter. For example, in the expression 3², the ² is the power.

Play this game to see how numbers increase when using powers.

• Using powers is a shorthand way of writing repeated multiplication using the same number. For example, rather than writing 4 x 4 x 4 it can be simplified to 4³. This is read as 'four to the power of three'.

• This sort of notation is used when finding the area of a square or the volume of a cube. It can also be used to describe other calculations using repeated multiplication.

• A power can also be known as an index or an exponent. An index, is the small floating number that goes next to a number or a letter. The plural of index is indices.

• Indices show how many times a number or letter has been multiplied by itself.

• Every expression has maths-specific language to describe each part. For example, 2⁷ is written in index form:

  • The 2 (larger digit) is called the base.

  • The 7 (smaller digit) is called the index number. Sometimes this is called the power or the exponent.

• When asked to calculate or work out the value of an expression that is written using power/index notation, some can be completed mentally, whilst other more complicated calculations would involve using a scientific calculator.

• All scientific calculators have a ‘power’ button. This is particularly useful when the index number is large.

Practise powers in this quiz.

Using powers is a strategy that is used in everyday life to help solve problems.

A painter or decorator may use powers to calculate and record the area of a square room. For example, a room in a house may measure 4.8 m x 4.2 m, this is an area of 20.16 square metres, this is written as 20.16 m².