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

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Exponents

Exponents

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

  • 23
  • 2^3
  • 2 to the power of 3

In this example, 3 is the exponent.

To compute the value of 23, you would multiple 2 to itself 3 times: 2 * 2 * 2. This evalutes to 8.

Common exponents have special names:

  • Exponent of 2 is often referred to as squared. So 32 is referred to as 3 squared, evaluating to 9.
  • Exponent of 3 is often referred to as cubed. So 23 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, 2-2 = 1/(2*2) = 1/4

More Examples

25 = 22222 = 32

-25 = -2*-2*-2*-2*-2 = 32

106 = 1,000,000

2-5 = 1/(22222) = 32