VG1
tall-og-algebra
Quiz
Powers and exponent rules
Powers are a shorthand for repeated multiplication. With the exponent rules you can simplify complex expressions quickly and efficiently.
What is a power?
aⁿ = a · a · a · ... · a (n times)
2⁴ = 2·2·2·2 = 16
Exponent rules
| Rule | Formula | Example |
|---|---|---|
| Product rule | aᵐ · aⁿ = aᵐ⁺ⁿ | 2³·2⁴ = 2⁷ = 128 |
| Quotient rule | aᵐ / aⁿ = aᵐ⁻ⁿ | 2⁵/2² = 2³ = 8 |
| Power of power | (aᵐ)ⁿ = aᵐⁿ | (2³)² = 2⁶ = 64 |
| Zero exponent | a⁰ = 1 | 5⁰ = 1 |
| Negative exponent | a⁻ⁿ = 1/aⁿ | 2⁻³ = 1/8 |
| Fractional exponent | a^(1/n) = ⁿ√a | 8^(1/3) = 2 |
Common mistake: The product rule only works when the base is the same.
Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate.
— Leonhard Euler (1707–1783)
🧠 Test yourself
Question 1 of 3
What is 2³ · 2⁴?