Arrange the given statements involving indices to show whether they are true or false.
\(x^{\frac12} \equiv \frac{x}{2}\)
\(x^{\frac32} \equiv x\sqrt{x} \)
\(9^{\frac23} \equiv 6\)
\(64^{\frac12} \equiv 32\)
\( 25^{\frac12} \equiv \frac15\)
\((1000)^\frac13 \equiv 10^{1}\)
\( x^{\frac12} + x^{\frac12} = 2\sqrt{x} \)
\( ( \sqrt{x})^4 \equiv x^2 \)
Your answer is not correct. Try again.
This is Laws of Indices  True or False? level 3. You can also
try:
Level 1
Level 2
Level 4
There are also a set of printable cards for an offline version.


Transum.orgThis 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: 

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 3 October 'Starter of the Day' page by Mrs Johnstone, 7Je: "I think this is a brilliant website as all the students enjoy doing the puzzles and it is a brilliant way to start a lesson." Comment recorded on the 11 January 'Starter of the Day' page by S Johnson, The King John School: "We recently had an afternoon on accelerated learning.This linked really well and prompted a discussion about learning styles and short term memory." 
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. 

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 MathsLearning 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 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! 
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. 
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/Alevel 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 donâ€™t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.
See the National Curriculum page for links to related online activities and resources.
\( 5^a \times 5^b \equiv 5^{a+b} \) \( 5^a \div 5^b \equiv 5^{ab} \) \( (5^a)^b \equiv 5^{ab} \) 
\( 5^1 \equiv 5 \) \( 5^0 \equiv 1 \) \( 5^{1} \equiv \frac15 \) \( 5^{2} \equiv \frac{1}{25} \) 
\( 5^{\frac12} \equiv \sqrt{5} \) \( 5^{\frac13} \equiv \sqrt[3]{5} \) \( 5^{\frac23} \equiv \sqrt[3]{5^2} \) 
Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you donâ€™t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.
Close