About this worksheet

This free Year 8 index laws worksheet is written for the Western Australian curriculum and mapped to SCSA content description WA8MNAA1. It targets one skill so students can practise until it sticks: by the end, students can say “I can multiply and divide powers with the same base, including terms with coefficients and pronumerals.”

What’s inside

• Key idea box – a short explanation with worked examples to read before starting.
• A · Fluency (16 questions) – quick practice to build accuracy.
• B · Core (10 questions) – worded problems set in everyday Australian contexts.
• C · Reasoning (4 questions) – explain, justify and spot the error.
• D · Challenge (4 questions) – harder multi-step and problem-solving questions for students ready to stretch.
• Separate marking key – every answer with working, plus mark allocations and marking criteria for reasoning questions.

Skills covered

• Adding indices when multiplying powers with the same base
• Subtracting indices when dividing
• Simplifying terms with coefficients such as 6a⁵b³ × 4a²b⁶

How to use this worksheet

Start with the Key idea box, then complete Section A (use a calculator only where a question says so). Most students should attempt Sections B and C; Section D suits students aiming for the top of the class or preparing for accelerated or extension maths. The worksheet is marked out of 58, and the score box on the last page helps students see which section needs more practice.

Common mistakes to watch for

• Multiplying the indices instead of adding
• Multiplying the bases, e.g. 3⁴ × 3² = 9⁶
• Applying the index laws to different bases
• Forgetting to multiply or divide the coefficients

Where this fits in the WA Year 8 sequence

Index Laws: Multiplying and Dividing Powers sits in the Algebraic techniques sub-strand of Number and algebra. It is one of a set of short, single-skill EduLift worksheets that split each Year 8 content description into sub-skills. Use the previous and next links to work through the sequence in order.

Common errors we see in tutoring

• Multiplying the indices instead of adding
• Multiplying the bases, e.g. 3⁴ × 3² = 9⁶
• Applying the index laws to different bases
• Forgetting to multiply or divide the coefficients