Indices

Indices are ways to write multiplications of the same number. For example:

The number 4 is called the power or index.

The first rule of indices is shown below:

This shows that two powers of the same base multiplied together is equal to the powers added together.
If you were asked to answer the below expression, the answer would be found using the first rule of indices.

The second rule of indices is shown below:

This shows us that the power of a power is equal to the powers multiplied together.
An example is shown below:

The third rule of indices is this:

This shows us that an index divided by another index is equal to the two indexes subtracted.
An example is shown below.

The fourth rule of indices is here:

Anything to the power of 0 is 1.

The fifth rule of indices is shown here.

For example, a to the power of a half is equal to the square root of a.