# The Laws of the Indices

## The Laws of the Indices

# Laws of Indices

### Basic Laws

- An
**index**tells us how many times a number is multiplied by itself. - Any number raised to the power of zero is equal to
**1**. For instance, 8^0 = 1. - Any number raised to the power of one is the number itself. For instance, 6^1 = 6.

### Multiplication and Division

- When multiplying terms with the same base,
**add**the indices. For instance, a^m x a^n = a^(m+n). - When dividing terms with the same base,
**subtract**the indices. For instance, a^m / a^n = a^(m-n).

### Power of a Power Rule

- When a term with an index is raised to another power,
**multiply**the indices. For instance, (a^m)^n = a^(mn).

### Negative Indices

- A term with a
**negative index**is equal to one divided by the same term with a positive index. So, a^-n = 1/ a^n.

### Fractional Indices

- A term with a
**fractional index**involves both roots and powers. For instance, a^(1/n) is the n-th root of a, and a^(m/n) is the n-th root of a, raised to the power m. - It’s important to remember that a square root could also be written as a^(1/2), a cube root as a^(1/3), and so on.