SOLUTION: [1/128]^-1/7

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Question 762788: [1/128]^-1/7
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!


If further explanations are needed:

The definition of power with a negative exponent for a positive base a and a real exponent x is as follows.
a%5E%28-x%29=1%2Fa%5Ex
So
If a=1%2F128, then 1%2F%28%281%2F128%29%29=128 and
%281%2F128%29%5E%28-1%2F7%29=128%5E%281%2F7%29

128=2%5E7 and one the properties of powers is that for a positive base a and real exponents x and y,
%28a%5Ex%29%5Ey=a%5E%28xy%29
so if a=128, x=7 and y=1%2F7, then
128%5E%281%2F7%29=%282%5E7%29%5E%281%2F7%29=2%5E%287%2A%281%2F7%29%29=2%5E1=highlight%282%29