Year 8 Maths • AC9M8N02 • Authored homework
Exponent laws
Practise Exponent laws through calculations, explanation, modelling and checking. Show reasoning in full sentences where useful, and check calculations or conclusions before finishing.
Part A
Short-answer questions
Simplify 3² × 3⁵.
Simplify 7⁶ ÷ 7² and explain the exponent law used.
Evaluate 12⁰ and explain why the answer is not 0.
A student writes 2³ × 2⁴ = 4⁷. Find and correct the error.
Write the rule or formula most useful for Exponent laws.
Show how to check one answer using estimation, substitution or inverse operations.
Write one common mistake students make in Exponent laws and correct it.
Create a small table, diagram or equation that represents this topic.
State where units, exact form or rounding matter in this topic.
Write one exam-style short question on Exponent laws and solve it.
Part B
Long-answer questions
Simplify (5²)³, 4³ × 4² and 9⁵ ÷ 9³, explaining the law used each time.
Write three equivalent expressions for 10⁶ using products, quotients or powers of powers.
Solve a multi-step problem involving Exponent laws and explain every step clearly.
Create a realistic word problem for Exponent laws, solve it and interpret the answer.
Compare two methods for a problem in Exponent laws and explain which is more efficient.
Write a worked solution that includes a check for reasonableness.
Create a problem with a deliberate trap, then solve it correctly and explain the trap.
Use a diagram, table, graph or equation to model a situation involving Exponent laws.
Explain how this topic connects to a previous Year 7 or Year 8 maths skill.
Write a full-mark response to a challenging Exponent laws question, including reasoning and final answer.
Part C
Research and understanding task
Research one real use of exponent notation such as file size, population, astronomy or area growth. Explain the meaning of the exponent.