GCSE · Indices

Zero and negative indicesExam-style questions

Why anything to the power zero is 1 (not 0), why a negative index means a reciprocal (not a negative number), and why a fraction raised to a negative power flips.

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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
    Write down the value of:

    (a) 505^0

    (b) 4−24^{-2}

    (c) (13)−1\left(\dfrac{1}{3}\right)^{-1}
    Level 3 · 3 marksTry it
  2. 2
    (a) Write 2−52^{-5} as a fraction.

    (b) Write 181\dfrac{1}{81} as a power of 3.
    Level 3 · 3 marksTry it
  3. 3
    Write down the value of:

    (a) 707^0

    (b) 10−310^{-3}

    (c) (14)−2\left(\dfrac{1}{4}\right)^{-2}
    Level 3 · 3 marksTry it
  4. 4
    Write these three numbers in order of size, smallest first:

    3−2303−13^{-2} \qquad 3^0 \qquad 3^{-1}
    Level 3 · 2 marksTry it