Laws of Indices - True or False?

Level 1Level 2Level 3Level 4Exam-StyleGameDescriptionHelpMore Indices

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

FALSE

$$(x^3)^4 \equiv x^7$$

$$\frac{x^6}{x^3} \equiv x^2$$

$$x^8 \div x^4 \equiv x^2$$

$$x^2 \times x^3 \equiv x^6$$

$$(x^3)^4 \equiv x^{12}$$

$$\frac{x^7}{x^3} \equiv x^4$$

$$x^8 \div x^5 \equiv x^3$$

$$x^2 \times x^3 \equiv x^5$$

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

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.

More Activities:

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 1 August 'Starter of the Day' page by Peter Wright, St Joseph's College:

"Love using the Starter of the Day activities to get the students into Maths mode at the beginning of a lesson. Lots of interesting discussions and questions have arisen out of the activities.
Thanks for such a great resource!"

Comment recorded on the 2 April 'Starter of the Day' page by Mrs Wilshaw, Dunsten Collage,Essex:

"This website was brilliant. My class and I really enjoy doing the activites."

Teacher! Are you delivering Maths lessons online?

Parents! Has home-schooling been thrust upon you at short notice?

Stay safe and wash yout hands!

Nine Digits

Arrange the given digits one to nine to make three numbers such that two of them add up to the third. This is a great puzzle for practicing standard pen and paper methods of three digit number addition and subtraction.

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:

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.

For Students:

For All:

Description of Levels

Close

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

 $$5^a \times 5^b \equiv 5^{a+b}$$ $$5^a \div 5^b \equiv 5^{a-b}$$ $$(5^a)^b \equiv 5^{ab}$$ $$5^1 \equiv 5$$ $$5^0 \equiv 1$$ $$5^{-1} \equiv \frac15$$ $$5^{-2} \equiv \frac{1}{25}$$ $$5^{\frac12} \equiv \sqrt{5}$$ $$5^{\frac13} \equiv \sqrt[3]{5}$$ $$5^{\frac23} \equiv \sqrt[3]{5^2}$$

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.

Close