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

\(2^x + 2^x \equiv 2^{x+1}\)

\( x^{a-b} \times x^{b-a} \equiv 1 \)

\( 8^{x} \equiv 4^{2x} \)

\( \frac{x^{\frac52}}{\sqrt{x}} \equiv x^5\)

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

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

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

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

Correct

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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.

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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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