This introduction covers The Rules of Powers 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 1 of 14 in this topic. Use this introduction to connect the idea to the wider topic before moving on to questions and flashcards.
The Rules of Powers
When scientists write the number of atoms in a mole (602,000,000,000,000,000,000,000), they use 6.02 × 10²³. When calculating compound interest or bacterial growth, we multiply powers together. Index laws are the rules that make working with powers quick and elegant, turning complex calculations into simple addition and subtraction.
Practice questions for Index Laws
Which of these is equivalent to a³ × a⁵?
Simplify a⁵ × a³
Quick recall flashcards
Division Law
aᵐ ÷ aⁿ = aᵐ⁻ⁿ
SUBTRACT the powers
Example: 5⁶ ÷ 5² = 5⁴
Zero Power Law
a⁰ = 1
ANY number to power 0 equals 1
(except 0⁰ which is undefined)
Examples: 5⁰ = 1, 100⁰ = 1