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\left(\frac{1}{10^{2}}\right)^{-2}
Rewrite 10^{2} as 10^{0}\times 10^{2}. Cancel out 10^{0} in both numerator and denominator.
\left(\frac{1}{100}\right)^{-2}
Calculate 10 to the power of 2 and get 100.
10000
Calculate \frac{1}{100} to the power of -2 and get 10000.