SOLUTION: Can someone please help me on this one? I have to simplify. (-8)^-4/3 The 8 is to the -4/3 power. Does that make sense? Thanks

Algebra ->  Algebra  -> Exponents-negative-and-fractional -> SOLUTION: Can someone please help me on this one? I have to simplify. (-8)^-4/3 The 8 is to the -4/3 power. Does that make sense? Thanks      Log On

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Question 43468: Can someone please help me on this one?
I have to simplify.
(-8)^-4/3
The 8 is to the -4/3 power. Does that make sense?
Thanks
Answer by aaaaaaaa(138) About Me  (Show Source):
You can put this solution on YOUR website!
The negative exponents follow a simple rule, that is:
x%5E%28-n%29+=+1%2F%28x%5En%29
Therefore -8%5E%28-4%2F3%29 can be simplified to 1%2F%28-8%5E%284%2F3%29%29.
I'm pretty sure that didn't help out much, but a definition on fractional exponents is probably going to clear things up. Remember this property:
x%5E%28p%2Fq%29+=+%28root%28q%2C+x%29%29%5Ep
Therefore, we can simplify to 1%2F%28root%283%2C+8%29%29%5E4%29%29. As we know, root%283%2C+8%29+=+2, so our answer is simplified to 1%2F%282%5E4%29. 2%5E4+=+16, so here is your answer: 1%2F16