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Don Leon ditanyakan dalam Science & MathematicsMathematics · 7 tahun yang lalu

How to find the unit digit of {(6)^26}^62 ?

2 Jawaban

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  • Paul
    Lv 4
    7 tahun yang lalu
    Jawaban Favorit

    As was mentioned above, the "units" digit will be 6 for any power of a positive integer ending in 6. This can be illustrated by showing that the product of any two such numbers ends in 6

    Consider any two (not necessarily distinct) positive integer "k_1" and "k_2" with the property that the unit digit is 6. Then there exist integers m and n such that:

    k_1 = 10m + 6 and k_2 = 10n + 6

    (k_1)*(k_2)

    = (10m + 6)(10n + 6)

    = 100 mn + 60m + 60n + 36

    = 10 [ 10mn + 6m + 6n + 3 ] + 6 (hence, it has an ending digit of 6)

    Now, since any (positive integer) power of such a number is simply a product of this number with itself (2 or more times) the product will also end in 6.

  • Anonim
    7 tahun yang lalu

    The units digit in any power of 6, or even a number ending in 6, is still 6. Check out few and you will see that.

    Numbers ending in 1 and 5 also have that property.

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