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\sqrt[12]{81^{-\frac{6}{7}}}
Use the rules of exponents to simplify the expression.
81^{-\frac{6}{7}\times \frac{1}{12}}
To raise a power to another power, multiply the exponents.
81^{-\frac{1}{14}}
Multiply -\frac{6}{7} times \frac{1}{12} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.
\frac{1}{3^{\frac{2}{7}}}
Raise 81 to the power -\frac{1}{14}.