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

Simplify each of the following exactly:

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

log_(8) 2

- math -
**Steve**, Saturday, October 27, 2012 at 1:12pm
#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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