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\left(-\frac{1}{27}\right)^{-9^{-\frac{1}{2}}}
Calculate 2 to the power of -1 and get \frac{1}{2}.
\left(-\frac{1}{27}\right)^{-\frac{1}{3}}
Calculate 9 to the power of -\frac{1}{2} and get \frac{1}{3}.
-3
Calculate -\frac{1}{27} to the power of -\frac{1}{3} and get -3.