SOLUTION: Evaluate this expression: (-32)^-3/5

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Question 279705: Evaluate this expression: (-32)^-3/5
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Two general rules are
a%5E%28-b%29+=+1%2Fa%5Eband
and
a%5E%28b%2Fc%29+=+%28a%5E%281%2Fc%29%29%5Eb%29
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applying these rules,
%28-32%29%5E%28-3%2F5%29+=+1%2F%28-32%29%5E%283%2F5%29
and
1%2F%28-32%29%5E%283%2F5%29+=+1%2F%28%28-32%29%5E%281%2F5%29%29%5E3
Note that the fifth root of -32 is -2 because
-2%2A-2%2A-2%2A-2%2A-2+=+-32, so
+1%2F%28%28-32%29%5E%281%2F5%29%29%5E3+=+1%2F%28-2%29%5E3
1%2F%28-2%29%5E3+=+1%2F%28-8%29
1%2F%28-8%29+=+-1%2F8 answer