This diagram covers Visual Understanding within Index Laws for GCSE Mathematics. Revise Index Laws in Number for GCSE Mathematics with 14 exam-style questions and 22 flashcards. This topic shows up very often in GCSE exams, so students should be able to explain it clearly, not just recognise the term. It is section 6 of 14 in this topic. Focus on the labels, the relationships between parts, and the explanation that turns the diagram into an exam-ready answer.
Visual Understanding
Why a⁰ = 1
Pattern:
2³ = 8
2² = 4 (÷2)
2¹ = 2 (÷2)
2⁰ = 1 (÷2)
Dividing by 2 each time
Multiplication Law
2³ × 2² = ?
(2×2×2) × (2×2)
= 2×2×2×2×2
= 2⁵
3 + 2 = 5 ✓
Negative Powers
2⁻³ = 1/2³ = 1/8
3⁻² = 1/3² = 1/9
10⁻¹ = 1/10 = 0.1
Flip to denominator!
Practice questions for Index Laws
Which of these is equivalent to a³ × a⁵?
Simplify a⁵ × a³
Quick recall flashcards
Zero Power Law
a⁰ = 1
ANY number to power 0 equals 1
(except 0⁰ which is undefined)
Examples: 5⁰ = 1, 100⁰ = 1
Division Law
aᵐ ÷ aⁿ = aᵐ⁻ⁿ
SUBTRACT the powers
Example: 5⁶ ÷ 5² = 5⁴