# Expanding Exponent Products

Hot air Balloons expand out to full size by filling them up with heated air.

In this lesson we are doing a different type of expanding out; one which involves two or more terms inside brackets that are raised to a power.

For two or more items inside brackets, that are then raised to a Power, we use the “Expanding Exponent Products Rule”.

This rule is kind of like a beefed up version of the Power of Power Rule.

At Passy’s World, we like to think of it as the Big Brother of the Power of Power Rule.

The Power of Power rule is used for when there is only one base item in the brackets, and works like this.

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Expanding Exponent Products Rule

In the following example we look at a two items in the brackets expansion, the “long way”, and then work it out using the Expanding Products Rule.

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Basically the Products Rule is as follows:

The Power outside the brackets needs to be applied to all Bases Inside the brackets.

Unlike other exponent rules, it is quite okay for these two bases to be different.

It is a lot like the Distributive Law, but is for Exponents.

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It is important not to confuse the Products Rule with the Power of Power Rule.

The Products Rule applies when we have more than one Base Item in the brackets.

If there is only one Base item in the brackets, we use the Power of Power Rule.

The Exponents Products Rule can look a lot like the Power of Power Rule, but always has two or more items in the brackets.

It is kind of like the Power of Power Rule’s Big Brother, as shown in the following example.

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Videos About the Exponent Products Rule

The following video shows the pattern whcih creates the Products Rule, and then does several examples.

The following video reviews the normal multiplication add rule, then covers Power of Power, and then at 4 minutes 28 seconds into the video, the Products Rule is demonstrated.

The following video also reviews the normal multiplication add rule, then covers Power of Power, and then around 5 minutes into the video, the Products Rule is demonstrated.

The following video shows how we can derive the Products Rule.

Expanding Exponent Products Rule – Examples

The following examples show how to apply the Expanding Exponents Product Rule when we have two or more base items in brackets raised to a power.

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

Image Copyright 2013 by Passy’s World of Mathematics

Image Copyright 2013 by Passy’s World of Mathematics

Product Rule Backwards for Simplifying

We can use the reverse of the product rule to combine two different bases, THAT ARE BOTH TO THE SAME POWER, into a single bracketed item.

The two different bases can be: two numbers, a number and a letter, or two letters; however it is required that both items are raised to the exact same Power.

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Product Rule Backwards – EXAMPLES

We can use the reverse of the product rule to combine two different bases, THAT ARE BOTH TO THE SAME POWER, into a single bracketed item.

The two different bases can be: two numbers, a number and a letter, or two letters.

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Exponent of Products Rule – SUMMARY

The following diagram summarises the forwards and backwards use of the Expanding Products Rule.

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