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Exponents and Repeated Multiplication

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Exponents and Repeated Multiplication

Exponents and Repeated Multiplication

Mathematical exponents illustration

📚 Part 1: Understanding Exponents

1. Match each repeated multiplication with its exponent form:
1. 3 × 3 × 3
2. 5 × 5 × 5 × 5
3. 2 × 2 × 2 × 2 × 2
4. 7 × 7
A. 2⁵
B. 7²
C. 3³
D. 5⁴
2. Circle the correct definition of an exponent:

The number that is added repeatedly

The small number showing how many times the base is multiplied by itself

The answer to a multiplication problem

The largest number in an equation

✏️ Part 2: Converting to Exponent Form

3. Write these repeated multiplications using exponent notation:

a) 4 × 4 × 4 × 4 = _______

b) 6 × 6 × 6 = _______

c) 10 × 10 × 10 × 10 × 10 = _______

d) 8 × 8 = _______

4. Write these exponents as repeated multiplication:

a) 2⁴ = _________________

b) 9³ = _________________

c) 5² = _________________

d) 3⁵ = _________________

🔢 Part 3: Calculating Powers

5. Calculate the value of these expressions. Show your working:

a) 3⁴ = ?

b) 2⁵ = ?

c) 5³ = ?

6. Which expressions equal 16? Check all that apply:

2⁴

16¹

🏗️ Part 4: Real-World Applications

7. Tile Pattern Problem:

A square tile pattern starts with 1 tile on each side. Each new layer adds tiles around the outside:

• Layer 1: 2 × 2 = 2² tiles

• Layer 2: 3 × 3 = 3² tiles

• Layer 3: 4 × 4 = 4² tiles

a) How many tiles are in Layer 5? Write using exponent notation: _______

b) Calculate the total number of tiles: _______

8. Draw a diagram to show what 2³ means using squares or dots:

📝 Part 5: Vocabulary and Understanding

9. Fill in the blanks using the words: base, exponent, power, repeated multiplication

In the expression 5³, the number 5 is called the __________ and the number 3 is called the __________. This expression is also called a __________ and it represents __________ __________.

10. Explain in your own words what 4² means:
11. True or False? Circle your answer and explain:

Statement: 3² and 2³ have the same value.

Answer: TRUE / FALSE

Explanation: ________________________________

🌟 Part 6: Challenge Questions

12. Powers of 10:

Complete the pattern:

10¹ = ______

10² = ______

10³ = ______

10⁴ = ______

What pattern do you notice? ________________________________

13. Problem Solving:

A bacteria culture doubles every hour. If you start with 2 bacteria:

• After 1 hour: 2² bacteria

• After 2 hours: 2³ bacteria

• After 3 hours: 2⁴ bacteria

How many bacteria will there be after 5 hours? Show your working:

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