Powers - BBC Bitesize

Key points

Using 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.

Powers activity

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

What are powers?

Using 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 of a cube. It can also be used to describe other calculations using repeated multiplication.

Examples

Skip image gallery

Image caption,
Powers can be used as a shorthand way of writing repeated multiplication of the same digits. 3 x 3 x 3 x 3 x 3 can be written as 3⁵. This is read as 'three to the power of five'.
Image caption,
7 x 7 x 7 x 7 can be written as 7⁴. This is read as 'seven to the power of four'.
Image caption,
Power notation is used when finding the area of a square or the volume of a cube. 16 is a square number. It can be written as 4 x 4 or 4². This is read as '4 squared'.
Image caption,
27 is a cube number. It can be written as 3 x 3 x 3 or 3³ . This is read as 3 cubed.

Using index form

A can also be known as an or an . 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 .
- The 7 (smaller digit) is called the number. Sometimes this is called the or the .

Examples

Skip image gallery

Image caption,
4⁶ is an example of an expression that has been written using index form. This is read as 'four to the power of six'.
Image caption,
The expression is made from two parts. The 4 (larger digit) is the base number. The 6 (smaller digit) is the index number (or power/exponent).
Image caption,
The number that is repeatedly multiplied is the 4 (the base number). The index of 6 means that 4 is used 6 times in the multiplication. 4 is the base and 6 is the index number. 4⁶ = 4 x 4 x 4 x 4 x 4 x 4
Image caption,
The expression is made from two parts. The 5 (larger digit) is the base number. The 3 (smaller digit) is the index number (or power/exponent). This is read as 'five cubed'.
Image caption,
The number that is repeatedly multiplied is the 5 (the base number). The index of 3 means that 5 is used 3 times in the multiplication. 5 is the base and 3 is the index number. 5³ = 5 x 5 x 5
Image caption,
Indices and powers are always written using the same type of notation. The base number can be represented by a number or a letter. The ‘a’ (larger digit) is the base number. The 4 (smaller digit) is the index number (or power/exponent). This is read as ‘a to the power of four'.
Image caption,
The value that is repeatedly multiplied is a (the base number). The index of 4 means that ‘a’ is used 4 times in the multiplication. ‘a’ is the base and 4 is the index number. a⁴ = a x a x a x a

Using a calculator

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.

Examples

Skip image gallery

Image caption,
Work out the value of 5 cubed.
Image caption,
Interpret the calculation using the base and the index number. 5 cubed means 5 x 5 x 5. A question like this can be solved without using a calculator.
Image caption,
5 is the base. 3 is the index (or power/exponent). 5³ = 5 x 5 x 5. 5 x 5 x 5 = 125
Image caption,
Work out the value of 12 to the power of five (12⁵). A question like this should be solved using a calculator.
Image caption,
Interpret the calculation using the base and the index number. Using a basic calculator type '12 x 12 x 12 x 12 x 12 ='. The answer should be 248,832
Image caption,
If using a scientific calculator to work out 12⁵, identify the power button. These appear differently, depending on the calculator.
Image caption,
To work out 12⁵ on a scientific calculator: type in the base (12), press the power button, enter the index (or power/exponent) (5), then press =
Image caption,
Using a calculator, 12⁵ = 248,832. 12 x 12 x 12 x 12 x 12 = 248,832

Question

Work out the value of 6 cubed.

Six cubed equals a highlighted question mark.

Practise powers

Practise powers in this quiz.

Quiz

Real-world maths

Man painting a wall with a roller — Image caption,
A decorator might calculate the area of a room to be painted.

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.

Man painting a wall with a roller — Image caption,
A decorator might calculate the area of a room to be painted.

More on Powers and roots

Find out more by working through a topic

3 of 3