GCSE · Indices

Fractional indicesExam-style questions

Why a power of 1/n is an nth root, how m/n means "root, then power", how negative fractional indices chain reciprocal + root + power, and how to solve equations by matching bases.

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

DifficultyAllLevel 3Level 4Level 5
  1. 1
    Evaluate:

    (a) 491/249^{1/2}

    (b) 271/327^{1/3}

    (c) 82/38^{2/3}
    Level 3 · 4 marksTry it
  2. 2
    Evaluate:

    (a) 1001/2100^{1/2}

    (b) 641/364^{1/3}

    (c) 321/532^{1/5}
    Level 3 · 3 marksTry it
  3. 3
    Evaluate 16−3/416^{-3/4}. Give your answer as a fraction.
    Level 4 · 3 marksTry it
  4. 4
    Evaluate (259)−1/2\left(\dfrac{25}{9}\right)^{-1/2}. Give your answer as a fraction.
    Level 4 · 2 marksTry it
  5. 5
    Evaluate:

    (a) 272/327^{2/3}

    (b) 813/481^{3/4}
    Level 4 · 4 marksTry it

6 more questions on fractional indices

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