# Arithmetic » What are powers?

## What is a power?

Powers are used to shorten calculations or formulas.
The calculation 7 × 7 × 7 × 7 × 7 can be shortened to 75.

You pronounce 75 as 'seven to the power of five' or as 'seven to the fifth'.

## Base and exponent

In 75, 7 is called the base and 5 is called the exponent.
So: baseexponent

## Special names

### Square

The 2 can be pronounced as square(d).
Therefore 72 can be pronounced as: 'seven squared'.

You can also use square as a verb.
So when you have to square –9, you have to do (–9)2 = 81.

### Cube

The 3 can be pronounced as cube(d).
Therefore 73 can be pronounced as: 'seven cubed'.

You can also use cube as a verb.
So when you have to cube –9, you have to do (–9)3 = –729.

## Examples

Numerical examples with an intermediate step*

52 = 5 × 5 = 25
–52 = –(5 × 5) = –25
(–5)2 = –5 × –5 = 25

83 = 8 × 8 × 8 = 512
–83 = –(8 × 8 × 8) = –512
(–8)3 = –8 × –8 × –8 = –512

* The intermediate step is not necessary to write down, however very useful for the explanation here.

Formula examples

A cube has edges/sides that always have the same length.
Therefore, you can make the following formulas and shorten them:
Volume = side × side × side = s3
Area = 6 × side × side = 6s2

Look for more formulas and graphs at power relation.