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Exponents and Order Operations

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Exponents and Order Operations worksheet preview

Exponents and Order of Operations

Mathematical symbols and exponents illustration

📚 Part 1: Understanding Exponents

1. What does 4³ mean?

4 × 3

4 × 4 × 4

3 × 3 × 3 × 3

4 + 4 + 4

2. Calculate: 2⁴ = __________

Show your working: 2⁴ = _____ × _____ × _____ × _____ = _____

3. Which expression equals 125?

3⁵

25²

4. Complete the pattern:

3¹ = 3, 3² = 9, 3³ = _____, 3⁴ = _____

🔢 Part 2: Order of Operations (GEMA)

Remember GEMA: Grouping, Exponents, Multiplication/Division, Addition/Subtraction

5. Evaluate: 3² + 4 × 2
6. Calculate: (2 + 3)² - 5
7. Solve: 6 × 2³ - 8 ÷ 4
8. Which operation do you do FIRST in this expression: 5 + 2³ × 4?

Addition (5 + 2)

Exponent (2³)

Multiplication (2 × 4)

🏠 Part 3: Real-World Applications

9. A square garden has sides of 4 metres. If you want to create 3 identical square gardens, what is the total area?

Expression: 3 × 4² = _______________ square metres

10. Extension Challenge: A traditional Māori weaving pattern uses squares arranged in layers. If each layer has 5² squares, and there are 2 layers plus 8 additional squares, how many squares are there in total?

Write the expression: ________________________

Calculate the answer: ________________________

11. Explain in your own words why we need to follow the order of operations.

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