exponents/ indices/ powers – the small numbers above a base number, representing how many times the base is multiplied by itself

To remember the meaning of exponents/ indices/ powers, use the following mnemonic:

In the seas (indices), my extraterrestrial opponent (exponent) had the power (powers) to multiply. 

Indices are a way of writing repeated multiplication in a compact form. When you write a number or variable with a small raised number, like 5³ or x⁴, the small raised number is the index (plural indices), which tells you how many times to multiply the base number by itself. 

For example:

5³ means 5 x 5 x 5 = 125

5³ = 125

Indices can also be negative, which represents the reciprocal of a number raised to the corresponding positive power. This means that any non-zero number raised to a negative power equals one divided by that number raised to the positive version of that power.

For example:

`x^-n = 1/(x^n)`

So, `2^-3 = 1/2^3 = 1/8`

There are a total of nine laws regarding indices that you need to know.