Indices for Singapore O-Level G3 Math
Add indices when multiplying the same base: a² × a³ = a⁵. Do not add indices when adding terms: a² + a³ cannot be combined by an index law. This guide shows which rule fits products, quotients, brackets and fractional powers.
What this guide covers
Positive, zero, negative and fractional indices and their laws. For the fractional-power examples here, bases are positive; zero cannot be raised to a negative power.
Syllabus reference: 2026 Mathematics 4052, N1, page 5. These are Mentora search groupings, not new official syllabus categories.
The content in this guide was also checked against 2027 G3 Mathematics K310, N1, page 5 on 2026-09-12. This is subject-content alignment, not a claim of complete syllabus coverage.
Use this guide for revision
What questions usually test
- Choose an index law from the operation: product, quotient, or power of a power.
- Use zero, negative and fractional indices with their stated restrictions.
- Simplify expressions without applying a law to addition or splitting a bracketed sum.
How to revise indices
Step 1
Name the operation
Check whether equal bases are multiplied, divided, or raised to another power.
Step 2
Apply one law at a time
Keep coefficients and restrictions visible; simplify only after the structure is clear.
Step 3
Check with a value
Test a small non-zero base to catch an invalid split or sign change.
Choose the index law from the operation
- Multiply: a² × a³ = a⁵
- Add the indices because the base is the same.
- Power: (a²)³ = a⁶
- Multiply the indices: three factors of a².
- Square root: a1/2 = √a
- A power of one half is a square root. For real-number examples here, use a non-negative base.
- Fractional index: am/n = (ⁿ√a)m
- The denominator gives the root and the numerator gives the power. For example, 272/3 = (∛27)² = 9.
- Add: a² + a³
- No index law combines these unlike terms. At a = 2 the sum is 12, not 2⁵ = 32.
- Brackets: (a + b)²
- An outside power applies to the whole bracket; it does not split into a² + b². Expand to obtain a² + 2ab + b².
- Reciprocal: a⁻² = 1/a²
- A negative index does not make the value negative. Require a ≠ 0.
Worked example
Simplify (2a³)² ÷ (4a), where a ≠ 0.
Square both factors: (2a³)² = 4a⁶. Then 4a⁶/(4a) = a⁵. The coefficient is squared too; the restriction remains because the original divisor is zero at a = 0.
Try three practice checks
Attempt each on paper before revealing the worked answer. These sample particular skills; they do not diagnose the whole topic or establish mastery.
Check 1
Evaluate 272/3.
Show worked answer
Take the cube root then square: 3² = 9.
Check 2
Simplify x⁰ + x⁻¹, where x ≠ 0.
Show worked answer
x⁰ = 1 and x⁻¹ = 1/x, giving 1 + 1/x. Adding indices here would be invalid.
Check 3
Is (a + b)² = a² + b² always true? Use a = 2, b = 3 to check.
Show worked answer
The left side is 25; the right side is 13. Expansion gives a² + 2ab + b², so the missing cross term is 2ab = 12.
Common mistakes to watch for
- Check that the bases are identical before adding indices in a product.
- Apply an outside power to the coefficient as well as the variable.
- Zero index gives 1 for a non-zero base, not 0; do not use this to assign a value to 0⁰.
If one of these occurs, compare the relevant step with the worked example, then try a different question before drawing conclusions.
You may need first
These verified prerequisite links suggest useful foundations. They do not make a claim about your current readiness.
Choose a useful next resource
Choose one step that matches the gap you just found.
Published by Mentora · Sources checked 12 Sept 2026
Editorial and source details
Original public examples and answers were checked with automated mathematical/editorial QA. No individual author, human reviewer or independent expert review is recorded.