# Recapping Laws of Indices

## Indices with algebra

As with numbers, the laws of indices also apply with algebra. Let’s recap and focus on some more difficult multiplication and division with indices.

**Multiplying indices**: a^{n} x a^{m} = a^{n+m}

**Dividing indices** a^{n} a^{m} = a^{n-m}

__Indices with brackets: __

(a^{n})^{m} = (a)^{n x m}

(ab)^{m }= (a)^{m }x (b)^{m}

**Negative indices:**

**Fractional Indices:**

**More complicated fractions:**

## Simplifying more complicated expressions

In the higher paper you will be expected to simplify more complicated indices that may combine indices, roots, brackets, fractions and algebra. Eg.

( The top being the numerator!)

- Simplify: √16v^5t^-6 / √64vt
- 1/2v^2
- 5√c^10d^15
- c^2d^3
- 1 / (4√m)^5
- m^-5/4