Posted by Remy on Saturday, October 27, 2012 at 11:33am.
#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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