GCSE Mathematics (9-1)
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    3.4 Negative and fractional indices — Practise with help

    Warm-up: remember

    1. Work out 64\sqrt{64}.
    2. Write 3−23^{-2} as a fraction.
    Answers and feedback
    1. 88, because 82=648^2=64.
    2. 19\frac{1}{9}, because 3−2=1/323^{-2}=1/3^2.

    Practise with help

    1. Work out 811/281^{1/2}.

    Hint

    An index of 12\frac12 means square root.

    One step

    811/2=8181^{1/2}=\sqrt{81}.

    Full working

    811/2=81=981^{1/2}=\sqrt{81}=9.

    2. Work out 1252/3125^{2/3}.

    Hint

    Take the cube root, then square the result.

    One step

    1252/3=(1253)2=52125^{2/3}=(\sqrt[3]{125})^2=5^2.

    Full working

    1252/3=(1253)2=52=25125^{2/3}=(\sqrt[3]{125})^2=5^2=25.

    3. Work out 8−4/38^{-4/3}.

    Hint

    Find 84/38^{4/3}, then take its reciprocal.

    One step

    84/3=(83)4=24=168^{4/3}=(\sqrt[3]{8})^4=2^4=16.

    Full working

    8−4/3=184/3=1168^{-4/3}=\frac{1}{8^{4/3}}=\frac{1}{16}.

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