SOLUTION: -8^-5/3 = -1/(8^5/3) = -1/(8^1/3)^5 = -1/32 What steps are being done between these answers?

Question 759572: -8^-5/3 = -1/(8^5/3) = -1/(8^1/3)^5 = -1/32 What steps are being done between these answers?

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
-8^(-5/3) = -1/(8^(5/3)) = -1/(8^(1/3))^5 = -1/32

The first two equal signs are just the definition of negative exponent and the definition of rational exponent (with a minus sign in front of each expression).
I cannot imagine any intermediate steps there.
Definition of rational exponent (for positive and positive integers and ):
or or or
I cannot imagine any intermediate steps there.
Definition of negative exponent (for any if is positive):

The last equal sign could be explained by

and
You could write out more in-between steps there, but I would think that anything more than
... = -1/(8^1/3)^5 = 1/2^5 = -1/32
is overkill.
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