Laws of Indices - True or False?

Level 1 Level 2 Level 3 Level 4 Exam-Style Game Description Help More Indices

Arrange the given statements to show whether they are true or false.

TRUE

FALSE

\(2^x + 2^x \equiv 2^{x+1}\)

\( x^{a-b} \times x^{b-a} \equiv 1 \)

\( 8^{x} \equiv 4^{2x} \)

\( \frac{x^{\frac52}}{\sqrt{x}} \equiv x^5\)

\( (2xy^3)^4 \equiv 2x^4y^{12}\)

\( (8x^3y^6)^\frac13 \equiv 2xy^2\)

\( \frac{x^3 + x^5}{x^4} \equiv x^{-1} + x\)

\( (x^2 + y^3)^2 \equiv x^4 + y^6 \)

Your answer is not correct. Try again.

Sad

This is Laws of Indices - True or False? level 4. You can also try:
Level 1 Level 2 Level 3

There are also a set of printable cards for an offline version.

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.

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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 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!!"

Comment recorded on the 8 May 'Starter of the Day' page by Mr Smith, West Sussex, UK:

"I am an NQT and have only just discovered this website. I nearly wet my pants with joy.
To the creator of this website and all of those teachers who have contributed to it, I would like to say a big THANK YOU!!! :)."

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

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Featured Activity

Roman Numerals Jigsaw

This is a wonderful activity for someone who does not know Roman numerals. By completing the activity an understanding of the symbols develops and a great sense of achievement is enjoyed.

Numeracy

"Numeracy is a proficiency which is developed mainly in Mathematics but also in other subjects. It is more than an ability to do basic arithmetic. It involves developing confidence and competence with numbers and measures. It requires understanding of the number system, a repertoire of mathematical techniques, and an inclination and ability to solve quantitative or spatial problems in a range of contexts. Numeracy also demands understanding of the ways in which data are gathered by counting and measuring, and presented in graphs, diagrams, charts and tables."

Secondary National Strategy, Mathematics at key stage 3

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 main page links to more activities designed for students in upper Secondary/High school.

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 site at Transum.info that contains most of the resources that are available here on Transum.org.

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

Description of Levels

Level 1 - The basic laws of indices

Level 2 - More complex statements including negative indices

Level 3 - More complex statements including fractional indices

Level 4 - Mixed puzzling statements for the expert

Cards - There are also a set of printable cards for an offline version of this activity.

Game - The Indices Pairs game with three levels of difficulty.

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

More on this topic including lesson Starters, visual aids and investigations.

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.

Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Examples

\( 5^a \times 5^b \equiv 5^{a+b} \)

\( 5^a \div 5^b \equiv 5^{a-b} \)

\( (5^a)^b \equiv 5^{ab} \)

\( 5^1 \equiv 5 \)

\( 5^0 \equiv 1 \)

\( 5^{-1} \equiv \frac15 \)

\( 5^{-2} \equiv \frac{1}{25} \)

\( 5^{\frac12} \equiv \sqrt{5} \)

\( 5^{\frac13} \equiv \sqrt[3]{5} \)

\( 5^{\frac23} \equiv \sqrt[3]{5^2} \)


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.		More Activities: Maths Map Go Maths Games Puzzles Times Tables TablesMaster iPad Maths Investigations Exam Questions
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 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!!" Comment recorded on the 8 May 'Starter of the Day' page by Mr Smith, West Sussex, UK: "I am an NQT and have only just discovered this website. I nearly wet my pants with joy. To the creator of this website and all of those teachers who have contributed to it, I would like to say a big THANK YOU!!! :)."		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 Jigsaw This is a wonderful activity for someone who does not know Roman numerals. By completing the activity an understanding of the symbols develops and a great sense of achievement is enjoyed.	Numeracy "Numeracy is a proficiency which is developed mainly in Mathematics but also in other subjects. It is more than an ability to do basic arithmetic. It involves developing confidence and competence with numbers and measures. It requires understanding of the number system, a repertoire of mathematical techniques, and an inclination and ability to solve quantitative or spatial problems in a range of contexts. Numeracy also demands understanding of the ways in which data are gathered by counting and measuring, and presented in graphs, diagrams, charts and tables." Secondary National Strategy, Mathematics at key stage 3
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 main page links to more activities designed for students in upper Secondary/High school.
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 site at Transum.info that contains most of the resources that are available here on Transum.org. When planning to use technology in your lesson always have a plan B!