Exponents & Indices
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Lesson overview
The full set of index laws, including negative and fractional exponents.
Go to lesson quiz →Exam guidance · WAEC WASSCE Paper 1 + Paper 2 Lens
Pacing
Objective speed on Paper 1 + structured step-by-step method marks on Paper 2 Theory/Practical.
How WAEC marks this
Examiners award method marks (M1) for stating the formula/definition and accuracy marks (A1) ONLY when SI units are written.
Watch out for
Writing bare numbers without working or omitting SI units loses up to 50% of Paper 2 marks even when the final value is right.
Lesson content
Overview — Exponents & Indices
The full set of index laws, including negative and fractional exponents. This lesson is at the beginner level — by the end, you'll be able to recognise this question type, apply a reliable method, and avoid the traps that cost marks.
Key Concept
The index laws govern how powers combine: a^m × a^n = a^(m+n), a^m ÷ a^n = a^(m−n), (a^m)^n = a^(mn), a^0 = 1, a^(−n) = 1/a^n, and a^(1/n) = ⁿ√a (the nth root of a). Further Mathematics tests the FULL set, including negative and fractional exponents, more rigorously than core WAEC Mathematics.
Why It's Tested This Way
Further Maths tests indices early because they underpin later topics — logarithms are literally the inverse of exponents, and simplifying surds/algebraic expressions throughout the syllabus depends on fluent index manipulation.
Method
To simplify an expression with indices, apply one law at a time, working systematically: combine same-base terms first using the addition/subtraction-of-exponents rules, then handle any powers-of-powers, then convert any negative or fractional exponents last.
Worked Example
Worked example: Simplify 2^5 × 2^(-2) ÷ 2^1. First combine using addition/subtraction of exponents: 2^(5 + (-2) - 1) = 2^2 = 4.
Second Worked Example
Second worked example: Simplify (8)^(2/3). Since 8 = 2^3, this becomes (2^3)^(2/3) = 2^(3 × 2/3) = 2^2 = 4 — converting to a common base makes a fractional exponent straightforward.
Common Traps
Common trap: applying a^m × a^n = a^(m+n) to terms with DIFFERENT bases (e.g. incorrectly simplifying 2^3 × 3^2) — the index laws for combining exponents only apply when the base is the SAME.
Lesson Summary
Remember: (1) identify what is being asked, (2) apply the WAEC strategy, (3) check against the traps. Complete the 10-question quiz below to unlock the next lesson — you need at least 60% to pass.
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