This is a summary of the rules of indices

sinceis not defined

(1) and(2)

(3) and (4)

When evaluating an expression like (4), find the root first because themay turn out to be a very large number.

(5) and(6)

(7) and(8)

The rules may be used as in the following examples:

Express 81 as a power of

Simplify

We apply in succession rules (5) and (6) above:

Arrange in order:

In order the list is