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.
