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 involving indices to show whether they are true or false.

TRUE

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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Description of Levels

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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/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.

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Curriculum Reference

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

Examples

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

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

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

\( 5^1 \equiv 5 \)

\( 5^0 \equiv 1 \)

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

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

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

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

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

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