# 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.

## FALSE

$$x^{\frac12} \equiv \frac{x}{2}$$

$$x^{\frac32} \equiv x\sqrt{x}$$

$$9^{\frac23} \equiv 6$$

$$64^{\frac12} \equiv 32$$

$$25^{-\frac12} \equiv \frac15$$

$$(-1000)^\frac13 \equiv 10^{-1}$$

$$x^{\frac12} + x^{\frac12} = 2\sqrt{x}$$

$$( \sqrt{x})^4 \equiv x^2$$

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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Interactive number-based logic puzzles similar to those featuring in daily newspapers designed to develop numeracy skills. These puzzles are drag and drop and can earn you a Transum Trophy.

## Numeracy

"Numeracy is a proficiency which is developed mainly in Mathematics but also in other subjects. It is more than an ability to do basic arithmetic. It involves developing confidence and competence with numbers and measures. It requires understanding of the number system, a repertoire of mathematical techniques, and an inclination and ability to solve quantitative or spatial problems in a range of contexts. Numeracy also demands understanding of the ways in which data are gathered by counting and measuring, and presented in graphs, diagrams, charts and tables."

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## Go Maths

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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 donâ€™t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

## Curriculum Reference

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

## Examples

 $$5^a \times 5^b \equiv 5^{a+b}$$ $$5^a \div 5^b \equiv 5^{a-b}$$ $$(5^a)^b \equiv 5^{ab}$$ $$5^1 \equiv 5$$ $$5^0 \equiv 1$$ $$5^{-1} \equiv \frac15$$ $$5^{-2} \equiv \frac{1}{25}$$ $$5^{\frac12} \equiv \sqrt{5}$$ $$5^{\frac13} \equiv \sqrt[3]{5}$$ $$5^{\frac23} \equiv \sqrt[3]{5^2}$$

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you donâ€™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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