Indices Cambridge IGCSE Mathematics revision
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In plain words
An index (or power) is shorthand for repeated multiplication: 2⁵ means five 2s multiplied together. A few rules let you combine powers without working everything out.
Three things to know
- Multiplying: add the powers, 2³ × 2⁴ = 2⁷. Dividing: subtract them, 2⁷ ÷ 2³ = 2⁴. A power of a power: multiply them, (2³)² = 2⁶.
- Anything to the power 0 is 1. A negative power means "one over": 5⁻² = 1/5² = 1/25.
- A fractional power is a root: 16^(1/2) = √16 = 4, and 8^(1/3) = ∛8 = 2.
Worked example
Work out 8^(2/3).
- The 3 on the bottom means cube root: ∛8 = 2.
- The 2 on the top means square: 2² = 4.
- 8^(2/3) = 4.
Tips and tricks
- The rules only work when the base is the same. 2³ × 3² can't be combined.
- A negative power does not make the answer negative. 2⁻³ is 1/8.
It lands in your notebook with its questions as flashcards.
Indices: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
What is 3⁴ × 3²?
Add the powers.
What is 7⁰?
Anything (except 0) to the power 0 is 1.
What is 2⁻³?
One over 2³.
What is 25^(1/2)?
A power of a half is a square root.
What is 10⁵ ÷ 10²?
Subtract the powers.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
3 questions, 6 marks. Write your answers on paper, then check them.
Indices
Cambridge IGCSE Mathematics 0580 · 6 marks · papermunch.org
Name ______________________________ Date ______________
Write 2³ × 2⁴ as a single power of 2, and work out its value.[2]
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2⁷ = 128.
Work out 5⁻² and 16^(1/2).[2]
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1/25 and 4.
Work out 27^(2/3).[2]
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9. ∛27 = 3, and 3² = 9.
Answers: Indices
- 1. 2⁷ = 128.
- 2. 1/25 and 4.
- 3. 9. ∛27 = 3, and 3² = 9.