Laws of Indices Explained: All 14 Laws with Examples - Negative, Fractional & Indicial Equations

The complete Laws of Indices lesson by ScholarNestHub. Every law is shown in letters, in words and with worked examples, from the zero index to solving indicial equations. If you want one video that covers all the laws of indices in order, this is it. 📘 WHAT YOU WILL LEARN PART A: BASIC LAWS (Laws 1 to 8) Law 1: Zero index, a⁰ = 1 (example: 75⁰ = 1) Law 2: Index one, x¹ = x (example: 13¹ = 13) Law 3: Negative index, y⁻ⁿ = 1/yⁿ (examples: 25⁻¹ = 1/25 and 5⁻² = 1/25) Law 4: Negative index of a fraction, (x/y)⁻ⁿ = (y/x)ⁿ (example: (3/2)⁻² = 4/9) Law 5: Fractional index (roots), m^(1/n) = the nth root of m (examples: 16^(1/2) = 4, 27^(1/3) = 3, 8^(2/3) = 4) Law 6: Power of a product, (ab)ⁿ = aⁿbⁿ (example: (3x²)² = 9x⁴) Law 7: Multiplication law, aᵐ × aⁿ = aᵐ⁺ⁿ (example: 2³ × 2² = 2⁵) Law 8: Division law, bˣ ÷ bʸ = bˣ⁻ʸ (example: 3⁷ ÷ 3⁵ = 3²) PART B: OTHER LAWS (Laws 9 and 10) Law 9: Power of a power, (aᵐ)ⁿ = aᵐⁿ (example: (2³)² = 64) Law 10: Power of a fraction, (a/b)ⁿ = aⁿ/bⁿ (example: (2/3)³ = 8/27) PART C: INDICIAL EQUATIONS (Laws 11 to 14) Law 11: Equal bases, equal powers. If aˣ = aʸ then x = y (example: solve 3^(x+1) = 81, so x = 3) Law 12: Equal powers, equal bases. If xⁿ = yⁿ then x = y (example: x³ = 5³, so x = 5) Law 13: Power equal to one. If aˣ = 1 then x = 0 (example: 7ˣ = 1, so x = 0) Law 14: Making the bases the same (example: solve 4ˣ = 8 by writing 4 = 2² and 8 = 2³, so x = 3/2) ⚠️ THE GOLDEN RULE Laws 7, 8, 9 and 11 work only when the bases are the same. Always check the bases first, make them the same, then use the law. 🎯 WHO THIS VIDEO IS FOR Junior and senior secondary school students (JSS3 to SS3), WAEC, NECO and JAMB candidates, Further Mathematics students, and anyone who needs a complete revision of indices. 📌 HOW TO GET THE MOST FROM THIS VIDEO 1. Copy each law and its example into your notebook. 2. Pause at each example and try it before the answer appears. 3. Re-watch Part C if indicial equations feel difficult. 4. Practise with your own examples using the same laws. 🌐 MORE FREE LEARNING RESOURCES Visit https://www.scholarnesthub.com for more step-by-step maths lessons, worked solutions and study materials. 👍 If this video helped you, LIKE it, SUBSCRIBE to ScholarNestHub and turn on the notification bell so you don't miss the next lesson. Share it with a classmate who needs it. 💬 Which law do you find hardest? Tell us in the comments and we will make a video on it. Presented by Idy James | ScholarNestHub: Empowering Academic Excellence Through Research. #LawsOfIndices #Indices #Mathematics #ScholarNestHub #MathsTutorial #WAEC #NECO #JAMB