SOLUTION: What are the steps to simplify this expression?(-27/8)^(-3/4) In word form: negative twenty-seven eighths to the power of negative three fourths. Is there a formula for these t

Question 970278: What are the steps to simplify this expression?(-27/8)^(-3/4)
In word form: negative twenty-seven eighths to the power of negative three fourths.
Is there a formula for these types of problems?
I came up with one(A^(-x/y) = ((a^x)^-1)^y), but it didn't work.
Thanks
Micah
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
That problem looks like there is a typo.

According to the usual definition,
any power with a exponent, or a exponent,
or any fractional exponent with an even denominator,
must have a positive base.
So, according to the definition of powers with fractional exponents
does not exist as a real number.
It is as undefined as .
Now, if we were working with complex numbers, maybe there would be a definition.

exists as a real number, but does not get really simple.

On the other hand,
exists as a real number and simplifies nicely.
Negative exponents are defined like this:
for and ,
and since we could say that
,
so it is a question of using the reciprocal of the base and changing the sign of the exponent.
====
= .
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