The **power ( ^)** operator (also known as the

*exponentiation*operator) allows you to raise a number to a higher power.

`number[base] ^ number[exponent] pow(number[base], number[exponent]) number[base].pow(number[exponent])`

In technical terms, it raises the first operand to the power of the second operand.

In Notion, the `^`

operator has a higher operator precedence than the unaryPlus and unaryMinus operators, and has **right-to-left** associativity.

You can also use the function version, `pow()`

.

## Example Formulas

```
3 ^ 4 /* Output: 81 */
pow(4,3) /* Output: 64 */
4.pow(3) /* Output: 64 */
2 ^ 2 ^ 3 /* Output: 256 - evaluates as 2 ^ (2 ^ 3) */
```

- \(x^0 = 1\)
- \((x^a)^b = x^{ab}\)
- \(x^{a^b} = x^{(a^b)}\)
*(not all languages respect this, but Notion does)* - \(x^a * y^a = (xy)^a\)
- \(x^a / y^a = (x/y)^a\)
- \(x^a * x^b = x^{a+b}\)
- \(x^a / x^b = x^{a-b}\)

### Exponent Associativity

In Notion, the `^`

operator has **right-to-left** associativity, which means that `x ^ y ^ z`

is evaluated as `x ^ (y ^ z)`

.

```
4 ^ 3 ^ 2 == 262,144
4 ^ (3 ^ 2) == 4 ^ 9 == 262,144
(4 ^ 3) ^ 2 == 64 ^ 2 == 4,096
/* Here's that last one according to the (x^a)^b == x^(ab) "Power Rule": */
(4 ^ 3) ^ 2 == 4 ^ (3*2) == 4 ^ 6 = 4,096
```

Not every programming and scripting language uses right-to-left associativity for serial exponentiation. Here’s a write-up comparing the methods for many popular languages. Even though standard mathematical notation has the **“Tower Rule”**, where \(x^{a^b} = x^{(a^b)}\) (aka: “Work top-down”), the computer science community has not come to a strong consensus on whether `x^y^z`

should be interpreted in the same way.

## Example Database

The table below shows exponentiation at work in a Notion database.

### View and Duplicate Database

### “Power” Property Formula:

```
prop("Base") ^ prop("Exponent")
```

Instead of using hard-coded numbers, I’ve called in each property using the `prop()`

function.