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\left(\left(-\frac{1}{2}\right)^{-4}\right)^{-1}
To raise a power to another power, multiply the exponents. Multiply 2 and -2 to get -4.
16^{-1}
Calculate -\frac{1}{2} to the power of -4 and get 16.
\frac{1}{16}
Calculate 16 to the power of -1 and get \frac{1}{16}.