📚 Part 1: Laws of Indices - Multiple Choice

1. What is the value of 2⁻³?

-8

1/8

-1/8

8

2. Simplify 5⁴ × 5⁻²

5²

5⁶

25

5⁻⁶

3. What is 16^(1/2)?

8

4

256

32

4. Which of these laws of indices are correct? (Select all that apply)

aᵐ × aⁿ = aᵐ⁺ⁿ

(aᵐ)ⁿ = aᵐⁿ

a⁻ⁿ = 1/aⁿ

aᵐ ÷ aⁿ = aᵐ⁻ⁿ

✏️ Part 2: Calculations and Problem Solving

5. Simplify the following expressions. Show your working:

a) 3⁵ × 3⁻² = _______________

b) (2³)⁻¹ = _______________

c) 27^(2/3) = _______________

6. Express 0.00045 in scientific notation using negative powers of 10:

7. A bacterial culture decreases according to the formula N = N₀ × (1/2)^(t/3), where t is time in hours. If the initial population N₀ is 8000 bacteria, how many bacteria remain after 6 hours?

🤔 Part 3: Reasoning and Explanation

8. Explain in your own words why a⁻ⁿ = 1/aⁿ. Use an example to support your explanation:

9. Create your own word problem that involves using fractional or negative powers. Then solve it:

10. Self-Assessment: Tick the success criteria you have achieved today:

I can correctly evaluate powers with positive exponents

I can correctly evaluate powers with negative exponents

I can correctly evaluate powers with fractional exponents

I can explain why negative powers correspond to reciprocals

I can use powers to express numbers in scientific notation

I can solve contextual problems involving powers

Laws of Indices Worksheet

Laws of Indices Worksheet

📚 Part 1: Laws of Indices - Multiple Choice

✏️ Part 2: Calculations and Problem Solving

🤔 Part 3: Reasoning and Explanation

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