Indices and Powers
Index laws are a key algebra and number skill. Students must also handle negative indices, making this a topic that bridges number work with algebraic manipulation.
What You'll Learn
- Applying multiplication and division index laws
- Understanding zero and negative indices
- Evaluating expressions with fractional indices
- Simplifying expressions using combined index rules
Watch Out For These Mistakes
Students make these errors again and again. Knowing them in advance gives you a head start.
Multiplying the indices instead of adding them when multiplying powers with the same base
Thinking a negative index makes the answer negative rather than a reciprocal
Confusing fractional indices with fractions of a number
What Examiners Say About Indices and Powers
Insights pulled from Cambridge IGCSE (0580) examiner reports — the exact mistakes candidates make every year.
- Misconception●●●●●
For time intervals crossing midnight, split into two parts: time until midnight + time after midnight. Remember an hour has 60 minutes, not 100.
Source: CIE 0580 · Feb/March 2024 · Paper 1 · Q5
- Common Mistake●●●●●
For compound interest, the rate and the number of periods must MATCH. 0.25% per month over 5 years = 60 monthly periods (not 5). Don't silently convert to annual — apply the rate as given.
Source: CIE 0580 · Feb/March 2023 · Paper 4 · Q1a(iii)
- Common Mistake●●●●●
When finding bounds, always give the final answer in the SAME UNITS as the variable in the question. If l is in metres, bounds must be in metres — convert at the end if your working was in cm.
Source: CIE 0580 · May/June 2023 · Paper 1 · Q18
Based on 3of 500+ insights extracted from CIE 0580 examiner reports (2018–2024).
Exam Coverage
This topic appears in the Cambridge IGCSE past papers. Our AI tutor can help with it on any question.
Useful for this topic:
Related Topics
Surds
Surds are irrational numbers left in root form. Students must simplify, add, subtract, multiply and rationalise surds, skills that also prepare them for further study in mathematics.
Standard Form
Standard form allows students to work with very large and very small numbers efficiently. It appears in science-context questions and is tested on both non-calculator and calculator papers.
Expanding Brackets
Expanding brackets (distribution) is a fundamental algebraic skill used across many topics. Students multiply each term inside the bracket by the term outside, progressing to double-bracket expansion and expressions raised to powers.
Related Articles
How to Read an Examiner Report (And Actually Use It)
Cambridge publishes a free examiner report for each IGCSE maths series, showing where students lost marks. Here is how to use them for targeted revision.
Online LearningTop 10 Online Maths Learning Platforms for Kids
Online math learning platforms have revolutionized how kids approach numbers and equations. These interactive tools make math fun, engaging, and accessible for
Maths EducationVirtual Reality Maths: Immersive Learning Experiences for the Digital Age
Imagine stepping into a 3D world where numbers come alive and equations float in mid-air. Virtual Reality (VR) is revolutionizing how students learn maths, maki
Ready to Master Indices and Powers?
Take our free diagnostic quiz to find out exactly where you stand, then practise number with our AI tutor.
Key number facts, rules, and formulae at a glance