GCSE Mathematics (9-1)
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    3.1 Powers and roots — Practise with help

    Warm-up: remember

    1. Work out 4×64\times6.
    2. Work out 727^2.
    Answers and feedback
    1. 2424, because 44 groups of 66 make 2424.
    2. 4949, because 72=7×77^2=7\times7.

    Practise with help

    1. Work out 343^4.

    Hint

    Write four factors of 3.

    One step

    34=3×3×3×33^4=3\times3\times3\times3.

    Full working

    34=3×3×3×3=813^4=3\times3\times3\times3=81.

    2. Work out 169\sqrt{169}.

    Hint

    Which positive integer squared gives 169?

    One step

    132=16913^2=169.

    Full working

    169=13\sqrt{169}=13, because 132=16913^2=169.

    3. Work out −643\sqrt[3]{-64}.

    Hint

    Find the number whose cube is −64-64.

    One step

    (−4)3=−64(-4)^3=-64.

    Full working

    −643=−4\sqrt[3]{-64}=-4, because (−4)3=−64(-4)^3=-64.

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