The Laws of Indices which apply to numbers are also applied to algebra. Consider `y^3 xx y^2`.

The term `y^3` can be expanded to `y xx y xx y`. The other term, `y^2`, can be expanded to `y xx y`. Therefore `y^3 xx y^2 = y xx y xx y xx y xx y`, which is equal to `y^5`.

This can be written as `y^a xx y^b = y^(a + b)`. When multiplying the same variable, add the powers. Note that the variable letter must be the same for both the terms being multiplied.

Division works in a similar way. The rule is written as `y^a ÷ y^b = y^(a - b)`. When dividing the same variable, subtract the powers. The example `e^6 ÷ e^3` can be shown as:

`frac(e^6)(e^2)`

`= frac(e xx e xx e xx e xx e xx e)(e xx e)`

`= frac(e xx e xx e xx e)(1)`

`= e^4`

The division rule leads to the fact that `e^0 = 1`. This can be shown by `e^2 ÷ e^2`

`= frac(e xx e)(e xx e)`

`= frac(e)(e)` (divided top and bottom by `e`)

`= 1` (divided top and bottom by `e` again)

which leads to the fact that any value to the power of zero equals 1.