# 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

$$2^x + 2^x \equiv 2^{x+1}$$

$$x^{a-b} \times x^{b-a} \equiv 1$$

$$8^{x} \equiv 4^{2x}$$

$$\frac{x^{\frac52}}{\sqrt{x}} \equiv x^5$$

$$(2xy^3)^4 \equiv 2x^4y^{12}$$

$$(8x^3y^6)^\frac13 \equiv 2xy^2$$

$$\frac{x^3 + x^5}{x^4} \equiv x^{-1} + x$$

$$(x^2 + y^3)^2 \equiv x^4 + y^6$$

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

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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