# Laws of Exponents & Indices & Powers

The laws of exponents, or laws of indices, or even power laws are all the rules we have to know on order to do operations with numbers raised to a power.

In this section we learn the rules for all the basic operations we need to know how to do with powers of numbers:

• multiplication
• division
• raising to a power

In mathematical terms that's $a^m + a^n = a^m + a^n$

and
$a^m - a^n = a^m - a^n$

Note: as such this is not much of a formula, it is nevertheless important as it helps us avoid making

## Multiplication Laws

#### Same Base

$a^m \times a^n = a^{m+n}$

#### Different Base

$a^m\times b^n = a^m \times b^n$ No simplication can be made.
exception
If exponents are equal $$m=n$$ $a^m\times b^m = \begin{pmatrix}a\times b \end{pmatrix}^m$

#### Example

$$3^2\times 3^5 = 3^{2+5} = 3^7$$