This worksheet extends the exponent laws to algebraic variables, teaching students to simplify expressions involving negative and zero exponents. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- Product rule: aᵐ × aⁿ = aᵐ⁺ⁿ. Quotient rule: aᵐ ÷ aⁿ = aᵐ⁻ⁿ. Power rule: (aᵐ)ⁿ = aᵐⁿ.
- Power of a product: (ab)ᵐ = aᵐbᵐ. These laws extend directly from numbers to variables.
- A negative exponent means "reciprocal": a⁻ⁿ = 1/aⁿ (for a ≠ 0).
- Any non-zero number or variable raised to the power 0 equals 1: a⁰ = 1.
- The exponent laws apply the same way whether exponents are positive, negative, or zero — combine exponents by adding, subtracting, or multiplying as appropriate.
What your child will practise:
- Applying the product and quotient rules to simplify expressions with the same base.
- Applying the power rule, including to expressions with multiple variables raised to a power.
- Evaluating and simplify expressions involving negative and zero exponents.
- Simplifying multi-step algebraic expressions combining several exponent laws.
- Solving an equation for an unknown exponent using the exponent laws.
Every section opens with a worked example, and the download includes a full answer key with step-by-step solutions and teaching notes on the mistakes students most commonly make.
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