Transum Software

Indices

A self marking exercise on indices including evaluating expressions and solving equations.

Menu L 1 L 2 L 3 L 4 L 5 Level 6 L 7 L 8 Challenge Exam-Style Help Game More
No calculator

This is level 6: mixed questions involving integer, negative and fractional indices. You will be awarded a trophy if you get at least 12 correct and you do this activity online.
Simplify the following.

\(4^{-\frac{1}{2}}\)

Correct Wrong

\(1^{-\frac{1}{2}}\)

Correct Wrong

\(1^{-\frac{1}{3}}\)

Correct Wrong

\(9^0\)

Correct Wrong

\(16^{-\frac{1}{2}}\)

Correct Wrong

\(25^{-\frac{1}{2}}\)

Correct Wrong

\(64^{-\frac{1}{3}}\)

Correct Wrong

\(16^{-\frac{1}{4}}\)

Correct Wrong

\(8^{-\frac{2}{3}}\)

Correct Wrong

\(64^{\frac{2}{3}}\)

Correct Wrong

\(1^{-\frac{2}{3}}\)

Correct Wrong

\(8^{-\frac{1}{3}}\)

Correct Wrong

\(27^{\frac{2}{3}}\)

Correct Wrong

\(16^{\frac{3}{4}}\)

Correct Wrong

\(27^1\)

Correct Wrong

Check

This is Indices level 6. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 5 Level 7 Level 8

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

Transum.org

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

Please contact me if you have any suggestions or questions.

Email address

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 25 June 'Starter of the Day' page by Inger.kisby@herts and essex.herts.sch.uk, :

"We all love your starters. It is so good to have such a collection. We use them for all age groups and abilities. Have particularly enjoyed KIM's game, as we have not used that for Mathematics before. Keep up the good work and thank you very much
Best wishes from Inger Kisby"

Comment recorded on the s /Coordinate 'Starter of the Day' page by Greg, Wales:

"Excellent resource, I use it all of the time! The only problem is that there is too much good stuff here!!"

Each month a newsletter is published containing details of the new additions to the Transum website and a new puzzle of the month.

The newsletter is then duplicated as a podcast which is available on the major delivery networks. You can listen to the podcast while you are commuting, exercising or relaxing.

Transum breaking news is available on Twitter @Transum and if that's not enough there is also a Transum Facebook page.

Featured Activity

Roman Numerals Quiz

Roman Numerals Quiz

You may understand our number system better by learning about another number system. A basic knowledge of Roman numerals will allow you to complete level one of this self marking quiz. Beyond level one will require a little more!

Answers

There are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer.

A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves.

Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members.

If you would like to enjoy ad-free access to the thousands of Transum resources, receive our monthly newsletter, unlock the printable worksheets and see our Maths Lesson Finishers then sign up for a subscription now:

Subscribe

Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

Maths Map

Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.

Teachers

If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes.

It may be worth remembering that if Transum.org should go offline for whatever reason, there are mirror sites at Transum.com and Transum.info that contain most of the resources that are available here on Transum.org.

When planning to use technology in your lesson always have a plan B!

Busolla, Australia

Saturday, August 22, 2020

"Thank you very much for providing these resources for free for teachers and students. It has been engaging for the students - all trying to reach their highest level and competing with their peers while also learning. Thank you very much!"

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

Apple

©1997-2020 WWW.TRANSUM.ORG

© Transum Mathematics 1997-2020
Scan the QR code below to visit the online version of this activity.

This is a QR Code

Transum.org/go/?Num=380

Description of Levels

Close

Close

Level 1 - Evaluating positive indices without a calculator

Level 2 - Evaluating positive indices with a calculator

Level 3 - Evaluating negative and zero indices

Level 4 - Multiplying, dividing and raising to another power

Level 5 - Evaluating indices expressed as fractions

Level 6 - Mixed questions involving integer, negative and fractional indices

Level 7 - Multiplying, dividing and raising to another power with coefficients

Level 8 - Solving simple equations involving indices

Indices Challenge - Dr Tim Honeywill has come up with these challenges to test your understanding of indices and algebra.

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

Game - Find the matching pairs of indices in this interactive online game.

Laws of Indices - a drag-and-drop true/false challenge.

More Indices including lesson Starters, visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up

Help Video

Examples

52 = 5 x 5 = 25

53 = 5 x 5 x 5 = 125

54 = 5 x 5 x 5 x 5 = 625

51 = 5

50 = 1

5-1 = 15

5-2 = 15x5 = 0.04

5a × 5b = 5a+b

5a ÷ 5b = 5a-b

(5a)b = 5ab

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up

Close

Close