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The Rules of Powers
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.
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Common Mistakes to Avoid
❌ Wrong: 2³ × 3² = 6⁵
✅ Right: Cannot combine - different bases
Index laws only work with same base
❌ Wrong: (2³)⁴ = 2⁷
✅ Right: (2³)⁴ = 2¹²
Multiply powers, don't add
❌ Wrong: 5⁰ = 0
✅ Right: 5⁰ = 1
Any number to power 0 equals 1 (except 0⁰)
❌ Wrong: 2⁻³ = -8
✅ Right: 2⁻³ = 1/8
Negative power ≠ negative number
Now try it yourself
Quiz · Question 1 of 14
Which of these is equivalent to a³ × a⁵?
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This topic in real past papers
Every real exam question we've found on index laws, with a full worked answer.
AQA Paper 1
Three of the four sittings we have full papers for test the laws of indices directly, and June 2019 tests it twice in the same paper.
Edexcel Paper 1
Two of the three sittings we have full papers for test the laws of indices directly, and June 2023 tests it twice in the same paper, once with numbers and once with algebra.