Arrange the given statements involving indices to show whether they are true or false.
\(x^{\frac12} \equiv \frac{x}{2}\)
\(x^{\frac32} \equiv x\sqrt{x} \)
\(9^{\frac23} \equiv 6\)
\(64^{\frac12} \equiv 32\)
\( 25^{\frac12} \equiv \frac15\)
\((1000)^\frac13 \equiv 10^{1}\)
\( x^{\frac12} + x^{\frac12} = 2\sqrt{x} \)
\( ( \sqrt{x})^4 \equiv x^2 \)
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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.


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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 don’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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