Learning pack · IGCSE handout

Indices

What's in this pack: printable worksheet PDF, matching answers PDF (IGCSE / Secure–Stretch practice). Index laws compress repeated multiplication: $a^m a^n=a^{m+n}$ , $(a^m)^n=a^{mn}$ , $a^0=1$ , $a^{-n}=1/a^n$ .

Resources at the top · full summary · videos with short notes below.

🎒 Resources in this pack

Jump straight to the printable files, or scroll to the summary and videos.

Scaffolded Learning Sheet — attempt the worksheet, then use the Answers for a full written solution.

📝 Open Learning Sheet ✅ Open answers 🎬 More topic videos (6)📖 Full summary

Files: 35_indices_handout.pdf · 35_indices_handout_answers.pdf

Full topic summary

Index laws compress repeated multiplication: $a^m a^n=a^{m+n}$ , $(a^m)^n=a^{mn}$ , $a^0=1$ , $a^{-n}=1/a^n$ .

Key learning points

Same base required to add/subtract indices when multiplying/dividing.
Fractional indices: $a^{1/n}=\sqrt[n]{a}$ , $a^{m/n}=(\sqrt[n]{a})^m$ .
Negative index means reciprocal, not a negative value.

Worked example 1 — Simplify

Simplify $a^3\times a^4$ .

Working

a^7

Add indices.

Worked example 2 — Division

Simplify $\frac{x^8}{x^3}$ .

Working

x^5

Subtract indices.

Worked example 3 — Negative index

Write $2^{-3}$ as a fraction.

Working

\tfrac{1}{8}

$a^{-n}=\frac{1}{a^n}$ .

🎬 Topic videos

Triangle of Power
3Blue1Brown · 8 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
Indeterminate: the hidden power of 0 divided by 0
Mathologer · 13 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
What is 0 to the power of 0?
Eddie Woo · 14 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Math Antics - Exponents and Square Roots
Math Antics · 11 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Math Antics - Intro To Exponents (aka Indices)
Math Antics · 10 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Algebra Basics: Exponents In Algebra - Math Antics
Math Antics · 12 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.

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