Prove the divisibility of the following numbers: 45^10·5^40 by 25^20

Question

Prove the divisibility of the following numbers: 45^10·5^40 by 25^20

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Hadley 4 weeks 2021-12-29T00:38:10+00:00 1 Answer 0 views 0

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    2021-12-29T00:39:45+00:00

    For this case we have the following expressions:

    45^{10} * 5^ {40} and 25^{20}

    Let:

    45^{10} * 5^ {40} (Integer m)

    25^{20} (Integer n)

    By definition, an integer m is divisible by an integer n if the remainder of the division is 0. That is, there is an integer p such that: m = n * p

    Rewriting the expression we have:

    25^{20} = 5^{2 * (20)} = 5^{ 40}

    So:

    \frac {45^{10} * 5^{ 40}} {5^{40}} =

    We cancel similar terms:

    45^{10}

    We check:

    45^{10} * 5^{ 40} = 5^{ 40} * 45^{ 10}

    Answer:

    If they are divisible

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