Algebra Powers Substitution

Will Power Race Car
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This car contains “Powers” – the power of a very hi-tech engine, as well as racing car driver “Will Power”.

When we substitute plenty of raw power into a racing car,including racing driver Will Power, we get some very large speeds produced around the track !

When we substitute numbers into Algebra Expressions that contain powers, we get a large number of multiplications to work out.

If you are not familiar with Indices, Exponents, and Powers, then the following lesson is compulsory preparation for what we are about to do here:


Working Out Steps for Powers

Here is a typical Powers substitution question:

Exponents Substitution 1
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The steps to working out all Powers substitution questions are as follows:

Exponents Substitution 2
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Powers need to be expanded using the basic exponents rule of multiplying the base out as many times as the small Index number says to do.

Exponents Substitution 3
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We also need to apply the Integers Operations Rules that are needed for multiplying and dividing positive and negative numbers.

Exponents Substitution 4
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Finally we also need to do our working out following the standard “Order of Operations”

Exponents Substitution 5
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Powers Substitution Video

Watch the following video which shows some typical substitution questions whcih involve exponents.


Powers Substitution Examples

The following examples show how to do some typical Powers Substitution questions.

Exponents Substitution 6
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Exponents Substitution 7
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Practical Example of Exponents Algebra

Algebra Formulas are used in the real world to work out the volume of various shapes.

Cylinders are a critical part of car engines, and the size of the motor is specified by the total volume of all of its cylinders.

Mechanics and Engineers need to know how to use Algebra Formulas.

The volume of each individual cylinder is calculated using the following Algebra formula:

Exponents Substitution Example

For example a car engine might be a 3.8 litre V6, or a 400 cubic inch V8.

The following example shows how to calculate the volume of a car cylinder, using Algebra substitution.

Exponents Substitution 9
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Values Table Substitution

We sometimes need to use a supplied rule equation to complete a values table of “x” and “y” values.

These tables are used when we need to draw a graph for the rule. However we will not be drawing the graph in this example.

This next example is basically four separate substitution questions, where we are putting our four answers into an answer table.

Exponents Substitution 10
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We now work out “y” answers for the other three “x” values the same way.

At Passy’s World we find it easiest to do these questions by adding a middle column to the table where we do the working out.

Exponents Substitution 11
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Related Items

Algebra Expressions
Algebra Terms Coefficients variables and Constants.
Algebra Substitution Using Positive Numbers.
Algebra Substitution Using Negative Numbers.
Basic Powers Exponents and Indices.
Real World Algebra Formulas
Survivor Algebra – Class Activity

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