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Multiplying Expressions with Indices

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Multiplying Expressions with Indices worksheet preview

Multiplying Expressions with Indices

Mathematical expressions with indices illustration

📚 Part 1: Foundation Skills

Success Criteria: I can apply the rule am × an = am+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 × px = p8, find the value of x.

x = ___________

Explain your reasoning:

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