Year 9 - Exponent laws - Free practice
Year 9 Exponent Laws Worksheets & Practice Tests
Index laws extended to variables and longer expressions.
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10 questions — 4 Foundation, 4 Standard, 2 Extension — with full worked solutions, calibrated to the Victorian Curriculum.
About this worksheet
Why we built it
Year 9 extends the exponent laws from Year 8 numbers to algebraic variables and longer expressions. These worksheets give your student practice mixing the laws in single questions - the format that catches them out on tests.
What's covered
Sub-skills your student will practise
- ✓Product, quotient and power-of-a-power laws applied to variables
- ✓Zero exponent in algebraic expressions
- ✓Negative exponents (preview)
- ✓Simplifying multi-step exponent problems
- ✓Mixed-rule questions with multiple bases
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Frequently asked
Questions parents ask about exponent laws
How are Year 9 exponent laws different from Year 8?
Year 9 extends the laws to algebraic variables and longer expressions. The same rules apply but students mix them in single questions: (2x^3)^2 x x^4 / x^5 needs three different laws.
What do students do when bases differ?
Index laws only work when bases match. 2^3 x 3^2 can't be simplified into a single power - it stays as 8 x 9 = 72. Students sometimes try to combine unlike bases and get it wrong.
What about negative exponents?
Year 9 introduces them as a preview: a^-n = 1/a^n. So 2^-3 = 1/8. They become more central in Year 10 once scientific notation arrives.
Is the zero exponent a Year 9 topic?
Yes - a^0 = 1 for any non-zero a. Introduced in Year 8, extended to variables in Year 9. Most students remember the rule but not why it's true (it follows from the division law).
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