To simplify \((-27)^{-2/3}\), we can follow these steps:
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Apply the negative exponent rule: \[ a^{-n} = \frac{1}{a^n} \] Therefore: \[ (-27)^{-2/3} = \frac{1}{(-27)^{2/3}} \]
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Evaluate \((-27)^{2/3}\): The exponent \(2/3\) can be interpreted as taking the cube root, then squaring the result.
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Finding the cube root: \[ \sqrt[3]{-27} = -3 \quad \text{(since } (-3)^3 = -27\text{)} \]
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Squaring the cube root: \[ (-3)^2 = 9 \]
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Putting it all together: Thus, we find: \[ (-27)^{2/3} = 9 \]
Now substituting back: \[ (-27)^{-2/3} = \frac{1}{(-27)^{2/3}} = \frac{1}{9} \]
So, the simplified result is: \[ \boxed{\frac{1}{9}} \]