We are trying to solve 27^{-2/3}. Firstly, using the index rule a^{xy}= (a^{x})^{y}, this can be rewritten as (27^{1/3})^{-2}. Lets tackle the value inside the bracket first: 27^{1/3} means the cube root of 27, and so is 3 (as 3^{3} = 27). Therefore we have 3^{-2}. Any value to the power of a negative becomes one over that value. As a result, we have 1/(3^{2}) = 1/9

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