This worksheet builds fluency with the exponent laws, teaching students to simplify expressions using the multiplication, division, power and zero-exponent rules. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- Product of powers rule: aᵐ × aⁿ = aᵐ⁺ⁿ — when multiplying powers with the same base, add the exponents.
- Quotient of powers rule: aᵐ ÷ aⁿ = aᵐ⁻ⁿ — when dividing powers with the same base, subtract the exponents.
- Power of a power rule: (aᵐ)ⁿ = aᵐˣⁿ — when raising a power to another power, multiply the exponents.
- Zero-exponent rule: a⁰ = 1 for any non-zero number a.
- The exponent laws only apply directly when the bases are the same — you can't combine 2³ × 3² this way.
What your child will practise:
- Applying the product rule to combine powers with the same base by adding exponents.
- Applying the quotient rule to combine powers with the same base by subtracting exponents.
- Applying the power-of-a-power rule by multiplying exponents.
- Recognising that any non-zero number raised to the power 0 equals 1.
- Combining multiple exponent laws in one expression, working through it step by step.
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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