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Powers and Index Laws: Year 8 maths

Students apply laws of indices to simplify expressions involving powers with common bases. The exercises cover multiplication, division, powers of powers, and negative or fractional exponents.

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What this covers

Powers and Index Laws is taught in Year 8 (age 12 to 13, KS3) as a topic to introduce. It sits in the Number strand.

Worked example

Simplify (x^5 × x^3) ÷ x^2.

  1. Apply the product rule to the numerator: x^(5+3) = x^8
  2. Apply the quotient rule: x^(8-2) = x^6
  3. The simplified result is x^6

Answer: x^6

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. Product and quotient laws with positive integer indices on a single variable
  2. Power of a power rule and zero index (e.g. (a^3)^2, b^0)
  3. Expressions with coefficients and multiple variables (e.g. 3a^2 × 4a^3)
  4. Negative integer indices (e.g. x^-2 = 1/x^2) and numerical evaluations
  5. 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.

  • Use positive integer powers and apply the laws of indices.

Sample sheet and answers

Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.

Powers and Index Laws

Year 8 maths

Qs
6
Marks
6
NameDateScore / 6
1.
Work out 22.
[1]
2.
Work out 32.
[1]
3.
Work out 22.
[1]
4.
Work out 22.
[1]
5.
Work out 22.
[1]
6.
Work out 53.
[1]

Answer key

  1. 42 × 2 = 4
  2. 93 × 3 = 9
  3. 42 × 2 = 4
  4. 42 × 2 = 4
  5. 42 × 2 = 4
  6. 1255 × 5 × 5 = 125