What this covers
Powers and Index Laws is taught in Year 12 (age 16 to 17, KS5) as a topic to introduce. It sits in the Number strand.
Worked example
Simplify (x^5 × x^3) ÷ x^2.
- Apply the product rule to the numerator: x^(5+3) = x^8
- Apply the quotient rule: x^(8-2) = x^6
- The simplified result is x^6
Answer: x^6
Difficulty scale
The sheet generator offers five difficulty settings for this topic.
- Product and quotient laws with positive integer indices on a single variable
- Power of a power rule and zero index (e.g. (a^3)^2, b^0)
- Expressions with coefficients and multiple variables (e.g. 3a^2 × 4a^3)
- Negative integer indices (e.g. x^-2 = 1/x^2) and numerical evaluations
- Fractional indices and combinations of roots and powers (e.g. 27^(23))
Common mistakes
- Multiplying the powers instead of adding them when multiplying bases (e.g. x^2 * x^3 = x^6)
- Applying the power to the coefficient without brackets (e.g. treating 2x^3 as (2x)^3)
Curriculum links
Indicative matches to National Curriculum for England. Check wording and codes against the official document.
- Manipulate algebraic expressions with negative and rational exponents using the laws of indices.