Standard form and indices are among the most searched IGCSE maths topics because they appear across algebra, number, and science-style questions. You need to use laws of indices ((a^m \times a^n = a^{m+n}), (a^m \div a^n = a^{m-n}), ((a^m)^n = a^{mn}), (a^0 = 1), (a^{-n} = 1/a^n), (a^{1/n} = \sqrt[n]{a})), and standard form ((A \times 10^n), (1 \leq A < 10)).

Laws of Indices – Quick Reference

• Multiply same base: add powers. Divide: subtract powers. Power of a power: multiply powers.
• (a^0 = 1); (a^{-n} = 1/a^n); (a^{1/2} = \sqrt{a}); (a^{1/n} = \sqrt[n]{a}).
• Simplify before substituting (e.g. write in single power of 2 or 3).

Standard Form

• Writing: One digit before decimal, rest after; (\times 10^n) (n positive for large numbers, negative for small).
• Calculating: Use calculator (EXP or EE key) or convert and use laws of indices; give final answer in standard form unless asked otherwise.
• Significant figures: Often “give to 3 s.f.” or “in standard form to 2 s.f.”

Practise mixed questions (indices + standard form) so you are confident in exams.

Worked Examples and Common Mistakes

Indices: Simplify 2³ × 2⁵ = 2⁸ (add powers). (3²)⁴ = 3⁸ (multiply powers). 5⁰ = 1. 2⁻³ = 1/2³ = 1/8. Standard form: 34000 = 3.4 × 10⁴. 0.0021 = 2.1 × 10⁻³. When calculating, use your calculator’s EXP or EE key or work in standard form and use laws of indices. Common mistakes: Wrong power (e.g. adding instead of multiplying when raising a power to a power); standard form with more than one digit before the decimal (e.g. 34 × 10³ should be 3.4 × 10⁴); wrong number of significant figures in the final answer. Give the answer in the form requested (e.g. “in standard form to 2 s.f.”).

Tutopiya Resources and Free Trial

Tutopiya’s IGCSE Maths tutors can help you master indices and standard form with targeted practice.

Book a free trial with an IGCSE Maths tutor or explore Tutopiya’s learning portal for free resources and number practice.

Ready to Excel in Your Studies?

Get personalised help from Tutopiya's expert tutors. Whether it's IGCSE, IB, A-Levels, or any other curriculum — we match you with the perfect tutor and your first session is free.

Book Your Free Trial