# 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

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

$$2^{-4} \equiv -16$$

$$\frac{x^4}{x^8} \equiv x^{-4}$$

$$3^{-3} \equiv -9$$

$$\frac{1}{x^{-1}} \equiv x$$

$$x^0 \equiv 0$$

$$\frac{1}{x^5} \equiv x^{-5}$$

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

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

There are also a set of printable cards for an offline version.

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## 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:

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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.

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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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