Index Laws Mastery
This lesson covers the fundamental laws of indices, moving from basic multiplication and division rules to more complex power of a power, zero, and negative indices. Students will learn to simplify algebraic and numerical expressions using these rules.
Learning objectives
- Apply the multiplication law (a^m × a^n = a^(m+n)) and division law (a^m ÷ a^n = a^(m-n)) to simplify expressions.
- Use the power of a power rule (a^m)^n = a^(mn) correctly.
- Understand and apply the zero index law (a^0 = 1) and negative index law (a^-n = 1/a^n).
Lesson plan (60 minutes)
Starter · 5 min
Do Now: Recap of square numbers and basic index notation (e.g., writing 5 x 5 x 5 as 5³).
Introduction · 15 min
Teacher instruction: Explain the multiplication and division laws using the explainer script and worked examples.
Guided Practice · 10 min
Guided practice: Students solve 4 'we do' problems on mini-whiteboards focusing on power of a power and zero index.
Independent Practice · 20 min
Independent Practice: Students work through differentiated worksheets (Support, Core, or Stretch).
Assessment · 10 min
Plenary: 8-question multiple-choice quiz to check for understanding and address misconceptions.
Key vocabulary
- Base
- The number or variable that is being multiplied by itself.
- Index
- The number that tells you how many times to multiply the base by itself. Also called power or exponent.
- Indices
- The plural of index.
- Multiplication Law
- When multiplying the same bases, add the powers.
- Division Law
- When dividing the same bases, subtract the powers.
Core worksheet (first questions)
- Simplify 2^5 x 2^2 x 2^4
- Simplify 10^8 / 10^5
- Simplify (y^6)^7
- Simplify 3x^2 x 4x^5
Quiz (sample)
1. Simplify 7^5 x 7^3 x 7^7
- A. 7^8
- B. 7^15
- C. 49^15
- D. 7^2
2. Simplify 4^8 / 4^6
- A. 4^12
- B. 4^24
- C. 4^2
- D. 1^2
3. Simplify (x^4)^5
- A. x^9
- B. x^1
- C. 20x
- D. x^20
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