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math

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Simplify each of the following exactly:


(8^(-1000) sqr2^10000)/16^500


log_(8) 2

  • math -

    #1:
    sqrt(10000) = 100
    16 = 8^(4/3), so 16^500 = 8^(2000/3)
    8^-1000 * 100 / 8^(2000/3)
    = 100 * 2^(-3000 - 2000)
    = 100 * 2^(-5000)

    #2:
    since 8 = 2^3, 2 = 8^(1/3)
    so, log_8(2) = 1/3

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