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The world’s population is exponentially increasing, especially in the world’s developing Countries.

Population Growth follows the Power of Power Rule, as shown in the example below.

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In this lesson we look at how to expand a single exponent item that is in brackets and raised to a Power.

There is a shortcut fast track rule for these expressions which involves multiplying the power values.

This rule is called the “Power of Power” Rule.

But first let’s look at expanding Power of Power without using this rule.

Expanding Power of Power – The Long Way

Let’s quickly review what a Power is, and how to expand a number raised to a power.

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Now let’s look at what we do to expand an Index item that is raised to a power.

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We can use this same multi-step expansion method for algebra letter variables.

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Expanding Exponents Using “Power of Power Rule”

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Let’s look at how we can do our two previous examples much faster by using this “Power of Power Rule”.

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Note that when using this rule, there must only be ONE item inside the brackets.

This item is either a Number raised to a power, or a letter variable raised to a power.

If there is more than one Base item in the brackets, we cannot use the Power of Power Rule.

(There is a Power of Products Expanding rule which we will cover in a later lesson for dealing with these type of expressions).

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Powers of Powers Videos

Here is a short simple video about the Power of Power Rule for indices and exponents.

In the following video the teacher develops the Power of Power Rule and then applies it to some expressions.

Power of Power Multiplications

The following examples show how to do Power of Power combined with multiplying terms.

These are basically a “two in one” expansion.

First we apply the Power of Power Rule, and then after this we apply the Multiply Rule.

Image Copyright 2013 by Passy’s World of Mathematics

Image Copyright 2013 by Passy’s World of Mathematics

This final Multiplication example shows that we need to remember that we can only add indices in the second step, if both bases, (the “Big” numbers), are exactly the same.

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Power of Power Divisions

The following examples show how to do Power of Power combined with dividing terms.

These are basically a “two in one” expansion.

First we apply the Power of Power Rule, and then after this we apply the Dividing Rule of subtracting exponents.

Image Copyright 2013 by Passy’s World of Mathematics

Image Copyright 2013 by Passy’s World of Mathematics

Image Copyright 2013 by Passy’s World of Mathematics

Power of Power Multiple Choice Game

The above free online multiple choice game will help you get better at Power of Power Expansions.

Click the link below to play this game.

http://www.slidermath.com/wjava/Expnt5.shtml

Related Items

Basic Indices and Exponents

Multiplying Exponents

Dividing Algebra Expressions

Dividing Exponents Using Subtraction Rule

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