SOLUTION: express each power asa radical,then evaluate. 4096^-5/6 I got so far =1/4096^5/6 =1_ (6√4096)^5 am i close?

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: express each power asa radical,then evaluate. 4096^-5/6 I got so far =1/4096^5/6 =1_ (6√4096)^5 am i close?      Log On


   

Question 262261: express each power asa radical,then evaluate.
4096^-5/6
I got so far =1/4096^5/6
=1_
(6√4096)^5
am i close?
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Here is the problem
4096%5E%28-5%2F6%29
step 1 - we can take the 6th root of 4096 as
4096%5E%281%2F6%29
we can rewrite 4096 as 2^12, so we get
%282%5E12%29%5E%281%2F6%29
using rules of exponents, we get
2%5E2 = 4
so, 4096%5E%281%2F6%29 is really 4.
step 2 - convert the negative into a positive as
4%5E%28-5%29 = %281%2F4%29%5E5
expand this base to get
1%2F1024