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Exponent Operations Practice

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Exponent Operations Practice

Mathematical exponent symbols and calculations

📚 Part 1: Laws of Exponents

1. Simplify: 4² × 4³

4⁵

4⁶

16⁵

16⁶

2. Calculate: 7⁶ ÷ 7²

7⁴

7⁸

1⁴

3. Which expressions equal 3⁷? (Select all that apply)

3³ × 3⁴

3⁹ ÷ 3²

3⁵ × 3²

3¹⁰ ÷ 3³

4. Simplify using the order of operations (GEMA): 2 × 5² × 5³

2 × 5⁵

10⁵

2 × 5⁶

10⁶

✏️ Part 2: Show Your Working

5. Calculate 6⁴ ÷ 6¹ and show your working using the division law for exponents.
6. Simplify the expression: 8² × 8⁵ × 8¹

Step 1: Apply the multiplication law: 8² × 8⁵ × 8¹ = 8^_____

Step 2: Calculate the final answer: 8^_____ = _________

7. Use estimation to check if your answer is reasonable for 3⁵.

I know that 3⁴ = _____, so 3⁵ should be approximately _____

My calculated answer: 3⁵ = _____

Is this reasonable? Explain: ________________________________

🧠 Part 3: Problem Solving

8. A scientist measures bacteria growth where the population doubles every hour. If there are initially 2³ bacteria, how many bacteria will there be after 4 more hours?

Expression: _____ × _____ = _____

9. Explain in your own words how to multiply powers with the same base. Use an example in your explanation.
10. Challenge: Simplify (4² × 4³) ÷ 4¹ and explain each step using correct mathematical vocabulary.

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