Basic Exponents and Indices

Image Source for iPad: http://www.mydigitallife.info

What do you notice about the numbers:

2, 4, 8, 16, 32, 64 ?

They are all computer memory and storage numbers, like
16 Gig, 32 Gig, 64 Gig on an iPad.

Power of 2 exponents are the basis of all computing which is done in “Binary” or base 2 numbers like these.

 

In this lesson we will be learning the basics of Indices, Powers, and Exponents.

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Here are some examples of Powers multiplication.

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Introductory Video on Exponents

Watch the following video which goes through the basics of Powers and Indexes (Indices).

 
 

Base and Index

The main idea with Powers is that we have a normal number, and then a superscript (raised up in the air) smaller number.

These two values then combine together to create a line of multilplications that need to be done.

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Squares Numbers

If we multiply a number times itself we get a “Square” number. These numbers are part of the normal times tables, and form the areas of square shapes.

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Cubic Numbers

If we multiply a number together three times, then we generate the volume of a cube.

These numbers are called “cube numbers” or “Cubics”.

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Index Expanded and Number Forms

There are three ways to write out Powers Terms.

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It is important to read mathematics questions carefully, so that we understand the form in which the final answer needs to be written.

 
 

Some Examples To Try

Here are some basic Powers questions for you to try.

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The answers to the above questions are as follows:

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The Power of Zero

In the previous examples, we saw that the power of one, means we just take the base once on its own.

The Power of Zero is not so easy to understand.

However Mathematicians have used patterns to work out that any number to the power of zero always equals 1.

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More Examples to Try

Here are some more Powers questions for you to try.

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The answers to the above questions are as follows:

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Algebra Powers

If we have Algebra letters instead of numbers in our question, it does not make much difference.

We still do Index Form and Expanded the Form the same way as we do for numbers.

However because we have letters, we cannot make a simplified whole number answer, so there is no “Numerical Form” for Algebra.

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It is easy to start getting confused as soon as we work with Algebra.

Make sure you are very clear on the difference between the following types of Algebra Terms.

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Interactive Online Exponents Lesson

This online activity does take a while to load in on the computer, but it is well worth the wait.

Be patient while the mostly blank screen loads the activity in.

This animated lesson on Exponents and Indices is excellent.

It goes through the basics, and even shows how to use the x to the power of y button on an interactive calculator to do powers questions.

Click the link below to do this interactive online lesson.

http://www.bbc.co.uk/schools/ks3bitesize/maths/number/powers_roots/activity.shtml

 
 

Videos About Exponents and Powers

Here is a great video by Mr Konst about Exponents.

 
 

The following video is part one of a quick general introduction to Exponent Form.

 
 

Here is the continuation part two of the previous video.

 
 

Worksheets on Exponents and Indices

Click the following links to access free worksheets on the Internet that cover basic Exponents questions.

http://www.ezschool.com/EZSheets/Algebra/Exponents/sheet14.html

http://www.ezschool.com/EZSheets/Algebra/Exponents/sheet15.html

http://www.ezschool.com/EZSheets/Algebra/Exponents/sheet6.html

http://www.mathworksheets4kids.com/exponent/find-missing-exponent-prime-base.pdf

http://www.mathworksheets4kids.com/exponent/find-missing-prime-base.pdf

 
 

Exponents Games

Try out each of these free online games to improve your exponent and powers skills.

 

Alien Exponents

In this game we click the spaceship which has the correct number answer on it to score each point.

If we get the question wrong, then the Alien makes it to earth and his team gets one point.

http://www.ezschool.com/Games/Exponents.html

 

Exponents Battleship

In this game we click on the right hand side grid to try and locate the enemy ships.

If we click where a ship is, then we are given an Exponents question to solve like this:

In this question, the ^ symbol means power.

1^4 means 1x1x1x1 and 3^1 means 3 so when we * multiply them together we have the correct answer of “3”.

Have fun playing this game by clicking the following link:

http://www.quia.com/ba/1000.html

 

Greater Than Less Than Game

In this game we pick and click the less than or greater than sign.

http://www.softschools.com/math/games/exponents_practice.jsp

 

Asteroids Game

This game is difficult at first as the screen is full of moving asteroids.

However as we get each question correct, it gets easier because there are less and less asteroids clogging up the screen.

http://www.mathdork.com/games/asteroidsexp3/asteroidsexp3.html

 

Exponents Matching Activity

In this activity we click on the left item, and then click on its matching right hand side item.

If we are correct, a mathcing line gets drawn. If we are incorrect, we have to try again.

http://www.studystack.com/matching-14392

 
 

Online Exponents Test

Now that we have watched all the videos, done some practice questions, and played all the games it is time to test our Basisc Exponents Skills.

Click the link below to do an exponents test online at the BBC Skillwise site.

http://www.bbc.co.uk/apps/ifl/schools/ks3bitesize/maths/quizengine?quiz=powers_roots&templateStyle=maths

 
 

Related Items

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

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