GCSE · Indices

The index lawsExam-style questions

Why multiplying powers adds the indices, dividing subtracts them, and a power of a power multiplies them — and why every part of a bracket, coefficient included, takes the power.

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15 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 1Level 2Level 3Level 4Level 5
  1. 1
    Simplify x3×x4x^3 \times x^4
    Level 1 · 1 markTry it
  2. 2
    Simplify y8y2\dfrac{y^8}{y^2}
    Level 1 · 1 markTry it
  3. 3
    (a) Work out the value of 34×3−23^4 \times 3^{-2} [1]

    (b) Work out the value of 272327^{\frac{2}{3}} [1]

    (c) Simplify (2x3)3(2x^3)^3 [1]
    Level 2 · 3 marksTry it
  4. 4
    (a) Simplify (2a3b)4(2a^3b)^4 (2 marks)
    (b) Work out the value of 8238^{\frac{2}{3}} (1 mark)
    Level 3 · 3 marksTry it
  5. 5
    Simplify:

    (a) x5×x3x^5 \times x^3

    (b) y9÷y3y^9 \div y^3

    (c) (z4)3(z^4)^3
    Level 3 · 3 marksTry it

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