Powers and roots
Cambridge IGCSE Mathematics (0580) · Unit 1: Number · 9 flashcards
Powers and roots is topic 1.4 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 1 — Number , alongside Types of number, Fractions, decimals and percentages and Operations and order of operations. In one line: An index (or exponent) indicates how many times a base number is multiplied by itself.
This topic is examined across Paper 1 (Core) or Paper 2 (Extended) — non-calculator — and Paper 3 (Core) or Paper 4 (Extended) — calculator.
The deck below contains 9 flashcards — 1 definition and 1 key concept — covering the precise wording mark schemes reward. Use the definition card to lock down command-word answers (define, state), then move on to the concept and application cards to handle explain, describe and compare questions.
'index' (or 'exponent')
An index (or exponent) indicates how many times a base number is multiplied by itself.
Questions this Powers and roots deck will help you answer
- › What does a negative index mean? Give an example.
What is the value of 5⁰?
Any non-zero number raised to the power of 0 is equal to 1. Therefore, 5⁰ = 1.
Simplify: x⁵ × x²
When multiplying indices with the same base, add the powers. x⁵ × x² = x⁵⁺² = x⁷
Simplify: y⁸ / y³
When dividing indices with the same base, subtract the powers. y⁸ / y³ = y⁸⁻³ = y⁵
What does a negative index mean? Give an example.
A negative index indicates a reciprocal.
What is the value of 9¹/²?
A fractional index of 1/2 represents the square root. Therefore, 9¹/² = √9 = 3.
Express 0.000047 in standard form (scientific notation).
Standard form is A x 10ⁿ, where 1 ≤ A < 10 and n is an integer. 0.000047 = 4.7 x 10⁻⁵
Simplify: (a³)⁴
When raising a power to another power, multiply the powers. (a³)⁴ = a³ˣ⁴ = a¹²
Define 'index' (or 'exponent').
An index (or exponent) indicates how many times a base number is multiplied by itself.
What is the cube root of 64?
The cube root of a number is a value that, when multiplied by itself three times, gives the original number. The cube root of 64 is 4, because 4 x 4 x 4 = 64.
Key Questions: Powers and roots
Define 'index' (or 'exponent').
An index (or exponent) indicates how many times a base number is multiplied by itself.
More topics in Unit 1 — Number
Powers and roots sits alongside these Mathematics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.
Cambridge syllabus keywords to use in your answers
These are the official Cambridge 0580 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.
Key terms covered in this Powers and roots deck
Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.
Related Mathematics guides
Long-read articles that go beyond the deck — cover the whole subject's common mistakes, high-yield content and revision pacing.
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