freeCodeCamp/guide/english/mathematics/exponents/index.md

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title: Exponents
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## Exponents                                                           
An exponent is shorthand for the the number of times a number is multiplied by itself.  It is often denoted with a superscript, karat, or with "to the power of" such as:

- 2<sup>3</sup>
- 2^3
- 2 to the power of 3

In this example, 3 is the exponent. 

To compute the value of 2<sup>3</sup>, you would multiply 2 to itself 3 times: 2 * 2 * 2. This evaluates to 8.

The general format of writing an exponent is:  
- base<sup># of times you multiply base by itself</sup>

Common exponents have special names:
- Exponent of 2 is often referred to as squared.  So 3<sup>2</sup> is referred to as 3 squared, evaluating to 9.
- Exponent of 3 is often referred to as cubed.  So 2<sup>3</sup> is referred to as 3 cubed, evaluating to 8.

### Negative Exponents
Negative exponents are computed similarly, except the value is placed as a denominator beneath a numerator of 1.

For example, 2<sup>-2</sup> = 1/(2*2) = 1/4

### More Examples 
2<sup>5</sup>  = 2*2*2*2*2 = 32

-2<sup>5</sup>  = -2*-2*-2*-2*-2 = 32

10<sup>6</sup> = 1,000,000

2<sup>-5</sup> = 1/(2*2*2*2*2) = 32