Evaluate the following?

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Answer 1 · 2016-10-26T18:59:51

#5/3#

First find each number as the product of its prime factors.
This is easier than it seems.

#390625# is divisible by 5. You will discover that

#390625 = 5xx5xx5xx5xx5xx5xx5xx5 = 5^8#

#6561 # is divisible by 3. You will discover that

#6561 = 3xx3xx3xx3xx3xx3xx3xx3 = 3^8#

#(390625/6561)^(1/8) = (5^8/3^8)^(1/8)#

Recall: #x^(1/8) = root8 (x)#

#(390625/6561)^(1/8) = (5^8/3^8)^(1/8) = root8(5^8/3^8)#

#= 5/3#