Mathematics - Exponentiation (square, cube) - Power

1 - About

Exponentiation is a mathematical operation involving two numbers:

  1. the base (b)
  2. the exponent (n) (or index or power).

<MATH> base^{exponent} = b^n </MATH>

It's a binary function.

3 - Example

<math> 2^3 = 2 * 2 * 2 = 8 </math>

4 - Pronunciation

The exponentiation <math>b^n</math> can be read as:

  • b raised to the n-th power,
  • b raised to the power of n,
  • b raised by the exponent of n,
  • most briefly as b to the n.

Example: The Exponent raises the first number, the base, to the power of the second number, the exponent.

Some exponents have their own pronunciation.

4.1 - Squared

<math>b^2</math> is usually read as b squared.

See Mathematics - Square (Quadratus) <math>a^2</math>

4.2 - Cubed

<math>b^3</math> is usually read as b cubed.

Cubing a number is the same as raising it to the third power.

5 - Law

<MATH>base^a * base^b = base^{a+b}</MATH>

6 - When the exponent (n) is

6.1 - a positive integer

When the exponent (n) is a positive integer, exponentiation corresponds to repeated multiplication.

<MATH> b^n = \underbrace{b \times \dots \times b}_{n} </MATH>

It's a product of n factors, each of which is equal to b (the product itself can also be called power):

6.2 - even

The exponents of a product are all even, the product is a perfect square.

Example: <math> 2^2*3^6 = (2*3^2)^2 </math>

7 - Inverse

The inverse of exponential is the root function

8 - Documentation / Reference


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