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\sqrt[3]{\frac{1}{8}\times 125^{-2}}
Calculate 16 to the power of -\frac{3}{4} and get \frac{1}{8}.
\sqrt[3]{\frac{1}{8}\times \frac{1}{15625}}
Calculate 125 to the power of -2 and get \frac{1}{15625}.
\sqrt[3]{\frac{1}{125000}}
Multiply \frac{1}{8} and \frac{1}{15625} to get \frac{1}{125000}.
\frac{1}{50}
Calculate \sqrt[3]{\frac{1}{125000}} and get \frac{1}{50}.