---
title: "Index laws: cheat sheet"
subtitle: "Irrational numbers and index laws"
---

# Index laws

> The words and methods from this unit, with an example of each.

:::keep-together

**index laws**: Write the powers out as factors to see why. Only powers of the same base combine.

$$a^m \times a^n = a^{m+n} \quad a^m \div a^n = a^{m-n} \quad (a^m)^n = a^{mn}$$

_3⁵ ÷ 3²: pairs of 3s cancel_

:::

:::keep-together

**zero index**: aⁿ ÷ aⁿ = 1, and the quotient law calls it a⁰.

$$a^0 = 1 \quad (a \ne 0)$$

:::