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: base^exponent

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.