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\frac{1}{\sqrt[4]{81}}
Use the rules of exponents to simplify the expression.
81^{\frac{1}{4}\left(-1\right)}
To raise a power to another power, multiply the exponents.
81^{-\frac{1}{4}}
Multiply \frac{1}{4} times -1.
\frac{1}{3}
Raise 81 to the power -\frac{1}{4}.