SOLUTION: this is the problem I have about simplifying radicals. the book is extremely complicated and I cannot figure these out. I would appreciate if someone explained their steps, so mayb

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Question 829745: this is the problem I have about simplifying radicals. the book is extremely complicated and I cannot figure these out. I would appreciate if someone explained their steps, so maybe I could understand how to do these more. thank you!
27^-2/3
over (fraction)
27^-1/3
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+%28+27%5E%28-2%2F3%29+%29+%2F+%28+27%5E%28+-1%2F3%29+%29+
------------------------------
First use the general rules:
+a%5E%28-b%29+=+1%2Fa%5Eb+
-------------------
Now what if you changed the right side to this:
+1%2Fa%5E%28-b%29+
What change would you have to make to the left side?
+a%5E%28-%28-b%29+%29+ is the change which is
+a%5Eb+, so now I have:
+a%5Eb+=+1%2Fa%5E%28-b%29+
---------------------
I can rewrite the problem as:
+%28+27%5E%28-2%2F3%29+%29%2A%28+1%2F%28+27%5E%28-1%2F3%29%29%29+
Now I can use the above general rule and rewrite as:
+%28+27%5E%28-2%2F3%29+%29%2A%28+27%5E%281%2F3%29+%29+
----------------------------
Now use the general rule:
+a%5Eb+%2A+a%5Ec+=+a%5E%28+b%2B+c+%29+
+27%5E%28+-2%2F3+%2B+1%2F3+%29+
+27%5E%28-1%2F3%29+
and now, using:
+a%5E%28-b%29+=+1%2Fa%5Eb+
+27%5E%28-1%2F3%29+=+1+%2F+27%5E%28+1%2F3%29+
+1%2F27%5E%281%2F3%29+=+3+ answer
--------------------------
My advice is to list the general rules that you
know in the form that I did and compare them
to the factors in your problem. Keep heading
in the direction of getting rid of minus
signs where you can.
Good luck


Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

this is the problem I have about simplifying radicals. the book is extremely complicated and I cannot figure these out. I would appreciate if someone explained their steps, so maybe I could understand how to do these more. thank you!
27^-2/3
over (fraction)
27^-1/3


27%5E%28-2%2F3%29%2F27%5E%28-1%2F3%29______27%5E%28-+2%2F3+-+%28-+1%2F3%29%29____27%5E%28-+2%2F3+%2B+1%2F3%29____27%5E%28-+1%2F3%29____1%2F27%5E%281%2F3%29____1%2F%28root+%283%2C+27%29%29_____highlight_green%281%2F3%29

You can do the check!! 



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