# Mathematics - Exponentiation (square, cube) - Power

Exponentiation is a mathematical operation involving two numbers:

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

$$base^{exponent} = b^n$$

It's a binary function.

## Example

$2^3 = 2 * 2 * 2 = 8$

## Pronunciation

The exponentiation $b^n$ 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.

### Squared

$b^2$ is usually read as b squared.

### Cubed

$b^3$ is usually read as b cubed.

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

## Law

$$base^a * base^b = base^{a+b}$$

## When the exponent (n) is

### a positive integer

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

$$b^n = \underbrace{b \times \dots \times b}_{n}$$

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

### even

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

Example: $2^2*3^6 = (2*3^2)^2$

## Inverse

The inverse of exponential is the root function