GCSE Mathematics (9-1)
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    3.3 Laws of indices — Practise with help

    Warm-up: remember

    1. Write 2×2×2×22\times2\times2\times2 as a power.
    2. Work out 525^2.
    Answers and feedback
    1. 242^4, because there are four factors of 2.
    2. 2525, because 5×5=255\times5=25.

    Practise with help

    1. Simplify a3a5a^3a^5.

    Hint

    Write the factors and count them.

    One step

    a3a5=a3+5a^3a^5=a^{3+5}.

    Full working

    a3a5=a8a^3a^5=a^8, because the product contains eight factors of aa.

    2. Simplify (b2)4(b^2)^4.

    Hint

    The whole group b2b^2 appears four times.

    One step

    (b2)4=b2×4(b^2)^4=b^{2\times4}.

    Full working

    (b2)4=b8(b^2)^4=b^8, because there are four groups of two factors of bb.

    3. Write 4−24^{-2} as a fraction.

    Hint

    A negative index means take the reciprocal.

    One step

    4−2=1424^{-2}=\frac{1}{4^2}.

    Full working

    4−2=142=1164^{-2}=\frac{1}{4^2}=\frac{1}{16}.

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