# 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

$$(x^3)^4 \equiv x^7$$

$$\frac{x^6}{x^3} \equiv x^2$$

$$x^8 \div x^4 \equiv x^2$$

$$x^2 \times x^3 \equiv x^6$$

$$(x^3)^4 \equiv x^{12}$$

$$\frac{x^7}{x^3} \equiv x^4$$

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

$$x^2 \times x^3 \equiv x^5$$

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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## 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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