Positive Indices Page 4

Powers of Powers

How would you simplify this? Click on the equation to see if you are right.

When you take a power of a power you multiply the indices.

Here are two ways to look at this.

		Using the definition.
		Using the Add the Indices Rule. Click.
		Since multiplication is repeated addition.

		Using the definition. Click.
		Using the definition again..
		Since multiplication can be done in any order and there are three groups of factors, and two fives in each group.

Lets summarize the rules we've looked at so far. These are sometimes called the three laws of indices.

If is any number and and are positive integers, then