Indices are a shorthand for writing multiplications of the same number.
\[ a^3 = a \times a \times a \]
The upper number is called the index, or power.
The lower number is called the base.
\[ a^p \times a^q = a^{p+q} \]
When multiplying powers of the same base we add the indices.
\[ a^p \div a^q = a^{p-q} \]
When dividing powers of the same base we subtract the indices.
\[ a^{-b} = \frac{1}{a^b} \]
A negative index represents 1 divided by the number.