FreePrintable
Laws of Indices Worksheet
A free, printable general worksheet ready for your classroom. Download instantly, print, and hand out to your students — no account needed.
Laws of Indices Worksheet
📚 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
About This Worksheet
Free Download
No sign-up, no email, no paywall. Just download and print.
Print-Ready
Formatted for standard paper. Clean layout, easy to read.
AI-Generated
Created with Kuraplan's AI, designed for real classroom use.
For Teachers & Parents
Use in classrooms, for homework, tutoring, or homeschool.
Need a custom version of this worksheet?
Kuraplan's AI generates custom worksheets in seconds — differentiated for every learner, aligned to your curriculum.
Generate Custom Worksheets — Free No credit card Curriculum-aligned Under 60 seconds
