math
posted by Remy on .
Simplify each of the following exactly:
(8^(1000) sqr2^10000)/16^500
log_(8) 2

#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