Question 876431
The exponents are -2/3 and -1/3


Subtract them to get -2/3 - (-1/3) = -2/3 + 1/3 = (-2+1)/3 = -1/3


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So that tells us 


<img src="http://www.sciweavers.org/tex2img.php?eq=%5Cfrac%7B27%5E%7B-2%2F3%7D%7D%7B27%5E%7B-1%2F3%7D%7D%20%3D%2027%5E%7B-1%2F3%7D&bc=White&fc=Black&im=jpg&fs=12&ff=arev&edit=0" align="center" border="0" alt="\frac{27^{-2/3}}{27^{-1/3}} = 27^{-1/3}" width="135" height="46" />


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Now simplify {{{27^(-1/3)^""}}} to get 


{{{27^(-1/3)^"" = 1/(27^(1/3)^"")}}}



{{{27^(-1/3)^"" = 1/(root(3,27))}}}



{{{27^(-1/3)^"" = 1/(root(3,3^3))}}}



{{{27^(-1/3)^"" = 1/3}}}


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In the end,


<img src="http://www.sciweavers.org/tex2img.php?eq=%5Cfrac%7B27%5E%7B-2%2F3%7D%7D%7B27%5E%7B-1%2F3%7D%7D%20%3D%20%5Cfrac%7B1%7D%7B3%7D&bc=White&fc=Black&im=jpg&fs=12&ff=arev&edit=0" align="center" border="0" alt="\frac{27^{-2/3}}{27^{-1/3}} = \frac{1}{3}" width="93" height="46" />