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\frac{1}{\left(-10\right)^{-2}}
Calculate 10 to the power of 0 and get 1.
\frac{1}{\frac{1}{100}}
Calculate -10 to the power of -2 and get \frac{1}{100}.
1\times 100
Divide 1 by \frac{1}{100} by multiplying 1 by the reciprocal of \frac{1}{100}.
100
Multiply 1 and 100 to get 100.