Year 8 - Exponents - Free practice
Year 8 Exponents (Index Laws) Worksheets
Multiply, divide, power-of-a-power - the four index laws.
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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
Index laws ("the exponent rules") trip up students because there are several of them and they look similar. These worksheets isolate each rule and then mix them up so your student learns to recognise which law applies before they start writing.
What's covered
Sub-skills your student will practise
- ✓Multiplying terms with the same base (a^m x a^n = a^(m+n))
- ✓Dividing terms with the same base (a^m / a^n = a^(m-n))
- ✓Power-of-a-power rule
- ✓Zero index (a^0 = 1)
- ✓Mixed-rule simplification problems
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Frequently asked
Questions parents ask about exponents
What are the four index laws?
(1) a^m x a^n = a^(m+n) when multiplying. (2) a^m / a^n = a^(m-n) when dividing. (3) (a^m)^n = a^(m x n) for power of a power. (4) a^0 = 1 for any non-zero base.
Why does anything to the power of zero equal one?
Because of the division law: a^n / a^n = a^(n-n) = a^0. But anything divided by itself is also 1. So a^0 = 1. This is the cleanest justification for an otherwise mysterious rule.
What gets students confused about index laws?
Adding exponents when they should be multiplying. (a^3)^2 is a^6, not a^5 - the rule is multiplication of exponents for a power of a power, not addition. Worksheets that mix all four laws are the only way to make this stick.
Are negative exponents Year 8?
Year 8 stays with integer and zero exponents. Negative exponents (a^-1 = 1/a) are formally Year 9, though many teachers preview them once the four basic laws are solid.
Want a real plan for the term?
Worksheets are great for repetition. A Tuterly tutor can spot the specific moves your student keeps getting wrong and fix them in one or two sessions.
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Talk to us about Year 8 exponents.
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