Multiplying Expressions with Indices

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Mathematical expressions with indices illustration

📚 Part 1: Foundation Skills

Success Criteria: I can apply the rule a^m × aⁿ = a^m+n to simple expressions

1. Simplify these expressions:

a) x² × x³ = ___________

b) y⁴ × y⁵ = ___________

c) a × a⁶ = ___________

2. Choose the correct answer for 2x³ × 3x²:

5x⁵

6x⁵

6x⁶

5x⁶

3. Multiply these expressions:

a) 4a² × 2a³ = ___________

b) 5m⁴ × 3m = ___________

✏️ Part 2: Developing Skills

Success Criteria: I can multiply expressions with different variables and combine like terms

4. Simplify these expressions with multiple variables:

a) 3xy² × 4x²y = ___________

b) 2ab³ × 5a²b = ___________

5. Expand and simplify:

a) 2x(3x² + 4x) = ___________

b) 3y²(2y³ - 5y) = ___________

6. Which of these are equivalent to 12x⁴y³? Tick all that apply:

3x²y × 4x²y²

6xy² × 2x³y

4x²y³ × 3x²

2x⁴ × 6y³

🚀 Part 3: Extension Challenges

Success Criteria: I can apply index laws to complex expressions and solve algebraic problems

7. Simplify these challenging expressions:

a) (2x³y)² × 3xy⁴ = ___________

b) 4a²b × 3ab³ × 2a³ = ___________

8. Problem solving: The area of a rectangle is given by 6x³y². If the length is 2xy, find an expression for the width in terms of x and y.

9. Extension: If p³ × p^x = p⁸, find the value of x.

x = ___________

Explain your reasoning:

Multiplying Expressions with Indices

Multiplying Expressions with Indices

📚 Part 1: Foundation Skills

✏️ Part 2: Developing Skills

🚀 Part 3: Extension Challenges

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