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Exploring Exponents and Powers

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Exploring Exponents and Powers

Mathematical powers and exponents illustration

🔢 Part 1: Understanding Exponents

1. What does 2³ mean?

2 + 3

2 × 3

2 × 2 × 2

3 × 3

2. Which expression equals 5⁴?

5 × 4

5 × 5 × 5 × 5

4 × 4 × 4 × 4 × 4

5 + 5 + 5 + 5

3. What is the value of 10²?

20

100

12

102

4. Fill in the blanks:

In the expression 3⁵, the number 3 is called the __________ and the number 5 is called the __________.

5. Complete the pattern for powers of 10:

10¹ = 10

10² = 100

10³ = __________

10⁴ = __________

✏️ Part 2: Calculating and Comparing Powers

6. Calculate these powers:

a) 2⁴ = ___________

b) 3³ = ___________

c) 5² = ___________

d) 4³ = ___________

7. Which is larger: 2⁵ or 5²? Show your work:
8. A computer scientist says that 2¹⁰ represents how many different combinations are possible with 10 switches that can each be on or off. Calculate 2¹⁰:

🌟 Part 3: Real-World Applications

9. A bacteria colony doubles every hour. If you start with 1 bacterium, write an expression using exponents to show how many bacteria there will be after 6 hours:
10. Explain in your own words why mathematicians use exponents instead of writing out all the multiplication. Give an example:
11. Create your own pattern using powers of 4. Write the first four powers and their values:

4¹ = ___________

4² = ___________

4³ = ___________

4⁴ = ___________

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