Why Is Anything to the Power 0 Equal to 1? | Exponent Rules

2³ = 8, 2² = 4, 2¹ = 2… so 2⁰ = 1? Zero copies of 2 should be nothing — so why is it one? In this video you'll SEE every exponent rule come from one simple idea: an exponent counts how many times you multiply. Count the factors, cancel the factors, and the rules write themselves — including the zero exponent and negative exponents. In this video you'll learn: ✔ What an exponent really means (2⁵ is NOT 2 × 5) ✔ Product rule: aᵐ · aⁿ = aᵐ⁺ⁿ (just count the factors) ✔ Quotient rule: aᵐ / aⁿ = aᵐ⁻ⁿ (cancel the factors) ✔ Why a⁰ = 1 — and why 2⁻¹ = ½ ✔ Power of a power (aᵐ)ⁿ = aᵐⁿ and power of a product (ab)ⁿ = aⁿbⁿ ✔ The traps: 2³ · 2⁴ ≠ 4⁷ and −2⁴ ≠ (−2)⁴ ✔ 3 examples from easy to SAT/GCSE level + a 5-second challenge ✔ Why folding paper 42 times would reach past the Moon ⏱️ CHAPTERS 0:00 2⁰ = 1?! The staircase 0:41 An exponent = repeated multiplication 1:23 Product rule: add the exponents 1:59 Quotient rule: subtract the exponents 2:36 Why anything to the power 0 is 1 3:25 Negative exponents: 2⁻¹ = ½ 4:09 Power of a power, power of a product 4:53 Example ladder 6:21 The trap: 2³ · 2⁴ = 4⁷? and −2⁴ vs (−2)⁴ 7:06 5-second challenge 7:42 Real world: fold paper 42 times → the Moon 8:32 Real world: KB, MB, GB as powers of 2 9:16 3-card recap 9:49 Wow fact: the paper-folding record ◀️ Previous: AL-02 · Algebraic Expressions ▶️ Next: AL-04 · One-Variable Equations 📚 Full playlist: The X Lab · Algebra 1 💬 Tell me in the comments: what is 3⁰ + 3⁻¹? 👍 If this helped, hit like and subscribe — new visual math every week. 🇪🇸 ¿Prefieres en español? → @AlgebrayTrigonometria #math #exponents #algebra #algebra1 #mathhelp #SATmath #GCSEmaths