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\left(\frac{\frac{1}{5}+7^{-1}}{2}\right)^{-1}
Calculate 5 to the power of -1 and get \frac{1}{5}.
\left(\frac{\frac{1}{5}+\frac{1}{7}}{2}\right)^{-1}
Calculate 7 to the power of -1 and get \frac{1}{7}.
\left(\frac{\frac{12}{35}}{2}\right)^{-1}
Add \frac{1}{5} and \frac{1}{7} to get \frac{12}{35}.
\left(\frac{12}{35\times 2}\right)^{-1}
Express \frac{\frac{12}{35}}{2} as a single fraction.
\left(\frac{12}{70}\right)^{-1}
Multiply 35 and 2 to get 70.
\left(\frac{6}{35}\right)^{-1}
Reduce the fraction \frac{12}{70} to lowest terms by extracting and canceling out 2.
\frac{35}{6}
Calculate \frac{6}{35} to the power of -1 and get \frac{35}{6}.