Arrange the given statements involving indices to show whether they are true or false.
\( (x^3)^4 \equiv x^7\)
\( \frac{x^6}{x^3} \equiv x^2\)
\(x^8 \div x^4 \equiv x^2\)
\(x^2 \times x^3 \equiv x^6\)
\( (x^3)^4 \equiv x^{12}\)
\( \frac{x^7}{x^3} \equiv x^4\)
\(x^8 \div x^5 \equiv x^3\)
\(x^2 \times x^3 \equiv x^5\)
Your answer is not correct. Try again.
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.


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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 12 July 'Starter of the Day' page by Miss J Key, Farlingaye High School, Suffolk: "Thanks very much for this one. We developed it into a whole lesson and I borrowed some hats from the drama department to add to the fun!" Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield: "I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information." 
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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.
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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.
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