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\left(\left(-\frac{1}{3}\right)^{-4}\right)^{-1}
To raise a power to another power, multiply the exponents. Multiply 2 and -2 to get -4.
81^{-1}
Calculate -\frac{1}{3} to the power of -4 and get 81.
\frac{1}{81}
Calculate 81 to the power of -1 and get \frac{1}{81}.