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\left(\frac{10^{2}}{1}\right)^{-1}
Multiply 10^{-5} and 10^{5} to get 1.
\left(\frac{100}{1}\right)^{-1}
Calculate 10 to the power of 2 and get 100.
100^{-1}
Anything divided by one gives itself.
\frac{1}{100}
Calculate 100 to the power of -1 and get \frac{1}{100}.